What is Perimeter: Definition and 115 Discussions

A perimeter is either a path that encompasses/surrounds/outlines a shape (in two dimensions) or its length (one-dimensional). The perimeter of a circle or an ellipse is called its circumference.
Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter; if the length of the string was exact, it would equal the perimeter.

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  1. nomadreid

    I The limit of the perimeter of a Koch snowflake as s(0) goes to zero

    On one side, if I have any finite value of s = the side of the original triangle of the Koch snowflake iteration, then the perimeter is infinite, so intuitively On the other hand, if I looked at the end result first and considered how it got there, then intuitively (Obviously at n=infinity and...
  2. S

    Find the minimum perimeter of a triangle with these constraints

    My attempt: $$|\vec{BA} -\lambda \vec {BC}| \geq 2|\vec {BC}|$$ $$|\vec {BA}|^2 -2 \lambda (\vec {BA} \cdot \vec {BC}) +\lambda ^{2} |\vec {BC}|^2 \geq 4|\vec {BC}|^2$$ $$|\vec {BA}|^2 -2 \lambda |\vec {BA}| \cos \theta +\lambda ^{2} \geq 4$$ Am I even on the right track? Thanks
  3. docnet

    Simple geometry problem -- Find the perimeter of the triangle ABC

    Hello, so I saw this problem on a website while looking up trigonometric identities and trying to solve it. what I know: The internal angles add up to pi Let the tangent point between A and B be X Let the tangent point between B and C be Y Let the tangent point between C and A be Z ##...
  4. crudux_cruo

    B Bug walking around the perimeter of a lazy susan (hypothetical)

    Given a bug that's walking counterclockwise around on the surface of a lazy susan (which itself is sitting on frictionless bearings), wouldn't the the friction between the bug and the lazy susan (which is needed to be able to walk) apply torque (no matter how negligible) that accelerates the...
  5. E

    Admissions Perimeter Scholar International 2021 Admissions

    Hi, I applied for the PSI masters program, but haven't heard back from them at all. My application status still says "in review". Anyone else in the same situation? I'm expecting a rejection, especially since I haven't been interviewed. But having no closure and feedback in such a long time is...
  6. A

    Perimeter relationships -- Dividing a rectangle into 4 triangles

    Hello, I am studying geometry with an app on my phone. There was a difficult problem, which had two different explanations for solving. I correctly understood one explanation. I reviewed later without memory of the problem at all. There was an obvious attempt from what was learned previously...
  7. A

    MHB Calculating Perimeter & Area of a Parallelogram & Triangle

    Find the perimeter and area of CD, if ABCE is a parallelogram and ADE is an equilateral triangle.
  8. anemone

    MHB Find length that minimizes the perimeter

    Let $ABC$ be an equilateral triangle and let $D,\,E$ and $F$ be the points on the sides $AB,\,BC$ and $AC$ respectively such that $AD=2,\,AF=1$ and $FC=3$. If the triangle $DEF$ has minimum possible perimeter, find $AE$.
  9. S

    B Why do shapes with the same area have different perimeters?

  10. clvsbr

    Programs How to decide between Perimeter Institute’s PSI and Cambridge’s MAST/Part 3?

    Hey guys, I’m gathering information in order to decide which master program to apply to (or, better, which one to go for in case I get admitted to both). I have read quite a lot online but it seems people who talked about PSI took it many years ago, while it was bright new and yet adjusting...
  11. H

    Admissions Critique my statement of purpose for Perimeter Scholar Program

    This is a draft of my SoP that I plan to send out to the Perimeter Institute for Perimeter Scholar Program. The program is designed for a 10-month duration focusing on theoretical physics. Please give opinion and suggestions for improving my statement of Purpose. ' Motivation and Research...
  12. E

    What is the perimeter of a rectangle with a 3:2 ratio and an area of 294 dm2?

    Hi. Could someone please help me with this? : A rectangle has a ratio of 3:2. The area is 294 dm2. What is the perimeter?
  13. Mathman2013

    Maximum area of a fenced-in half a circle

    . Homework Statement Let imagine you have gras field formed as a semi circle and you want to fence in that area. The fence is connected to a wall, so you only have to fence in the area formed by the semi-circle. You have to use 60 meters of fence bought at a hardware store. Homework...
  14. I

    Programs Which Graduate Program in Theoretical Physics is Right for Me?

    Hello. I'm currently studying theoretical physics and planning to continue my study in theoretical physics. I know that there are two interesting places to pursue the education in this field, the International Center for Theoretical Physics (pre-PhD program), and the Perimeter Institute for...
  15. R

    MHB Finding the Perimeter of an Odd Shape.

    I have been looking around for information on how to find the perimeter of an odd shape, but I can't find any explanations that seem to fit because the given shape is partially rounded. I already know the answer is 16 + 2\pi but I am unsure how they came to it. I'm guessing they get 16 from 7 +...
  16. M

    MHB Did I Calculate the Perimeter of A Sector Correctly?

    A sector has the following: radius = 5 inches angle = 30° I was told to use the formula in the picture. My answer is P = 10.05 inches. The book's answer is P = 12.62 inches. Am I using the right formula?
  17. A

    Finding the approximate change in the perimeter of a circle

    Homework Statement The radius of a circle increases from 3 to 3.01 cm. Find the approximate change in its perimeter. Here's a link to the actual question, in case you need the answer for 6(a) to solve 6(b) http://imgur.com/a/nQt6M Homework Equations Perimeter of circle = 2πr Area of circle =...
  18. T

    What is the perimeter of triangle APQ in this geometry problem?

    Homework Statement there is a circle with radius 9cm centred at o segment oa is 15cm ab, ca and pq are tangents to circle at points b,c and r respectively find perimeter of triangle apq Homework EquationsThe Attempt at a Solution i have solved the problem and got the right answer with two...
  19. M

    MHB Find Perimeter of Rectangle with Given Area and Width

    Given the width of a rectangle whose area is 25ft^2 is x, find the perimeter of this rectangle. Let me see. A = L•W 25 = L•x 25/x = L P = 2L + 2W P = 2(25/x) + 2x P = (50/x) + 2x Is this right? If it is right, use the inequality below to show that P ≥ 20. In the following inequality, a...
  20. M

    MHB What is the perimeter of triangle ABC?

    The vertices of triangle ABC are A(1, 1), B(9, 3), and C(3, 5). 1. Find the perimeter of triangle ABC. I must use the distance formula for points on the xy-plane to find all three sides. I then add all three sides. Correct? 2. Find the perimeter of the triangle that is formed by joining the...
  21. P

    MHB Perimeter of Smallest Rectangle

    The perimeter of the smallest rectangle that can be formed using 24 squares 1cm2 of area each is
  22. O

    Calculate circle radius with segment height and perimeter

    (mentor note: posted in a non-homework forum hence no template) Hello! I have a problem I'm trying to solve. I'm transforming a circle with known radius. Knowing it's radius i can calculate the circumference. I transform it by squeezing one side, leveling it, creating a circle segment with a...
  23. CynicusRex

    Minimum of x+1/x (Perimeter Square < Perim equal area rects)

    Homework Statement Gelfand - Algebra p.115 problem 264: Prove that a square has the minimum perimeter of all rectangles having the same area. Hint. Use the result of the preceding problem. Homework Equations Preceding problem: Prove that a square has the maximum area of all rectangles having...
  24. M

    MHB What is the Perimeter of Triangle ABC?

    The vertices of Triangle ABC are A(1, 1), B(9, 3), and C(3, 5). Find the perimeter of Triangle ABC. I need to find the distance of AB, BC, and AC. I then must add all three distances to find the perimeter. Correct?
  25. K

    MHB Ratio Of Area To Perimeter

    The length of a rug is eight times greater then the width. if the width of the rug is (w+5), what is the ratio of the area of the rug to the perimeter of the rug in simplest form?
  26. Const@ntine

    Object is dragged across a semicircle's perimeter

    Homework Statement A small object with mass m is dragged without friction to the highest point of a semicircle with a radius of R, by a weightless rope. a) If the magnitude of his velocity is constant, then his acceleration that is parallel to the semicircle, is zero. Prove that F = mgcosθ...
  27. M

    Comp Sci Program in C++ calculate area and perimeter of rectangle.

    1. Homework Statement calculate the area and perimeter of 2 rectangles(two objetcs and one builder), print the sides, area and perimeter, the function printrectangle must identify which side belongs to base and height... the teacher suggest this in private: float side1 float side2 and this in...
  28. I

    Programs Perimeter Institute Undergraduate summer program 2016

    Hi, has anyone applied to Perimeter Institute 2016 Undergraduate summer program? I just wonder how competitive this program is.
  29. Albert1

    MHB Minimum Perimeter of a Trapezoid: Find R & P

    a trapezoid $ABCD,$ with $\overline {AD}// \overline {BC}, \overline {AB}=\overline {CD}$, and diagonal $\overline {AC}=15=\overline {BD}$ if R is its maximum area ,please find : (1)R (2)find its minimum perimeter P
  30. L

    MHB Formulas for Triangle Perimeter & Height

    Write the following formulas: a) The minimum perimeter of any triangle (abc) only known heights corresponding to the sides a and b. b) The maximum height and minimum corresponding to the side b of any triangle (abc) only known the value of its perimeter and height corresponding to the side a.
  31. L

    MHB Calculate the area of a triangle knowing its perimeter and 2 heights

    Calculate the area of a triangle knowing its perimeter and 2 heights perimeter = 30 m ha = 8 m hb = 9 mNOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 41.29 m2 B) 42.93 m2 or 36.28 m2 C) 42.95 m2 or 36.29...
  32. L

    MHB Calculating Isosceles Triangle Side Length with Perimeter & Area

    That value has to have one side of a triangle to be isosceles knowing its perimeter and area. Area = 40 m2 Perimeter = 30m NOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 13.33 m B) 19.18 m or 4.54 m C)...
  33. L

    MHB Calculate the sides of a triangle knowing its area, perimeter and angle A.

    Calculate the sides of a triangle knowing its area, perimeter and angle A. Area = 30 m2 Perimeter = 30m Angle A = 30º NOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 6.09, 9.36 and 14.55 B) 7.40, 8.63 and...
  34. A

    Why isnt Cauchy's formula used for the perimeter of ellipse?

    So the formula for an ellipse in polar coordinates is r(θ) = p/(1+εcos(θ)). By evaluating L = ∫r(θ) dθ on the complex plane on a circle of circumference ε on the centered at the origin I obtained the equation L = (2π)/√(1-ε^2). Why then does Wikipedia say that the formula for the perimeter is...
  35. H

    Perimeter Institute Course Videos & Tutorials: Accessible to Everyone?

    I'm watching some of the course video of the Perimeter International Scholar, and the professor always mention the wiki that their students can assess. Is there any way that I can assess too? I really want to read some of the lecture notes and tutorial. Thank you!
  36. L

    MHB Very dificult: The minimum perimeter and maximum height of a triangle under constraints

    Obtain -The maximum height corresponding to the side b of any triangle (abc) once known the value of its perimeter and height corresponding to the a side a. -The minimum perimeter of any triangle (abc) once known the heights corresponding to the a and b sides. Aux: Geogebra construction...
  37. I

    Perimeter institute 2015 summer undergrad program

    Hey, I am from UC Berkeley. I wonder if anyone here has applied to perimeter institute's 2015 summer program. I've applied but haven't heard back from them yet. I wonder if anybody here has got a reply.
  38. Nathanael

    Probability of a point in a square being 0.5 from perimeter

    Homework Statement Consider a square of side length 1. Two points are chosen independently at random such that one is on the perimeter while the other is inside the square. Find the probability that the straight-line distance between the two points is at most 0.5. 2. The attempt at a solution...
  39. D

    Maximum area of a triangle inscribed in another triangle?

    Homework Statement [/B] Hello! I have this question which I don't quite know how to solve... ABC is an equilateral triangle - the length of its sides equal to (a). DE is parallel to BC 1. What length should DE be to achieve the largest possible area of triangle BDE? 2. What length should DE...
  40. N

    Area of hexagon is maximum while perimeter is fixed

    this is the given problem: and this is my attempt at a solution: I am stuck here as the variable y is unknown and I want to express y in terms of x, but cannot figure out how to do so. Thanks for any help!
  41. S

    MHB How do we find the dimensions of a rectangle given its perimeter and diagonal?

    Hi, I can do basic quadratics but don't know how to apply them to the following problems: The perimeter of a rectangle is 34cm. Given that the diagonal is of length 13cm and the width is \(x \)cm, derive the equation \(x^2-17x+60=0\). hence find the dimensions of the rectangle. (My first go...
  42. B

    MHB Help with Geometry: Volume, Area and Perimeter of Pyramid

    Hello . I am in the end of my exams and i have to do a geometry figure like a pyramid ( view image ) below Now i should find the Perimeter, Volume and Surface of this figure . Lengths are all 5 cm, Can somebody find and write the Permiter,volume and surface for this figure please it's urgent...
  43. Saitama

    MHB Maximum area of triangle and quadrilateral - given perimeter

    Problem: Let $0<a<b$ i)Show that amongst the triangles with base $a$ and perimeter $a+b$, the maximum area is obtained when the other two sides have equal length $b/2$. ii)Using the result (i) or otherwise show that amongst the quadrilateral of given perimeter, the square has maximum area...
  44. E

    MHB Determine the ratio of the base to the perimeter.

    8) An isosceles triangle has two sides of length 9x+3. The perimeter of the triangle is 30x+10 a) Determine the ratio of the base to the perimeter, in simplified form. State the restriction on x Thanks for your help!
  45. T

    How to calculate the wetted perimeter

    Homework Statement So I have been taught that the wetted perimeter is the perimeter in which the surface is wet. So in the case for internal forced convection of a thick wall pipe I would have thought the perimeter would be 2*pi*r where r is the inner radius of the pipe. However, doing a bit...
  46. M

    Schools MSc in theoretical physics: Imperial College or Perimeter Institute?

    I'm considering both the MSc in Quantum Fields and Fundamental Forces at Imperial and the Perimeter Scholars International program at Perimeter. I do not currently live in the UK or Canada (or even Europe or North America...) I want to continue to a PhD, possibly at the same place I did my...
  47. anemone

    MHB Find the perimeter of the triangle

    The two shortest sides of a right-angled triangle, $a$ and $b$ satisfy the inequality \sqrt{a^2-6a\sqrt{2}+19}+\sqrt{b^2-4b\sqrt{3}+16}\le3. Find the perimeter of this triangle.
  48. MarkFL

    MHB Unknown's question at Yahoo Answers regarding the perimeter of a rectangle

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  49. A

    Rate of change of area of a square with respect to its perimeter

    oops I meant "Rate of change of area of a square with respect to its side length" Ok I have to use this annoying Stewart textbook for my Calc class in college. Most of the questions require what I like to call "Monkey Math," where you just memorize a set of steps and then follow them rigidly...
  50. jfy4

    Does the Area Law Always Hold True in Lattice Gauge Models?

    While reading through Kogut's lattice gauge theory introduction he goes through the area and perimeter laws for lattice gauge models. The result is something like this \left\langle \prod _{l\in C}\sigma_{3}(l) \right\rangle \sim \exp(-P) for low temperature, and \left\langle \prod...
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