Need help on a very simple geometry problem

  • Thread starter Thread starter Modernization
  • Start date Start date
  • Tags Tags
    Geometry
AI Thread Summary
A regular hexagon's side length is described as twice the square root of its apothem. The initial calculations suggested that the side length is represented as 2 times the square root of "a," where "a" is the apothem. However, confusion arose regarding the definition of "a," leading to incorrect conclusions about the relationship between the side and apothem. Suggestions were made to clarify the variables and consider alternative methods for solving the problem, including using numerical values. The discussion emphasizes the importance of precision in mathematical definitions and calculations.
Modernization
Messages
9
Reaction score
0

Homework Statement


a side of a regular hexagon is twice the square root of its apothem. Find the length of the apothem and the side

Homework Equations


a formula for special triangle
90 degree side is doubled the 30 degree side, and 60 degree side is root 3 times the 30 degree side

The Attempt at a Solution



after drawing the pictures and do the math, i got:
side: 2 times square root of a; a stands for apothem, an unknown value
apothem: square root of a times square root of three
 
Physics news on Phys.org
How about making a formula for the ratio length of side and apothem? Replace the side length of the hexagon from the info. Solve.
 
Modernization said:

Homework Statement


a side of a regular hexagon is twice the square root of its apothem. Find the length of the apothem and the side


Homework Equations


a formula for special triangle
90 degree side is doubled the 30 degree side, and 60 degree side is root 3 times the 30 degree side

The Attempt at a Solution



after drawing the pictures and do the math, i got:
side: 2 times square root of a; a stands for apothem, an unknown value
apothem: square root of a times square root of three

In your second line, you say that "a stands for apothem" (You mean that a stands for the length of the apothem- let's be precise!) but in the third line you say "apothem: square root of a times square root of three". Obviously a is not the length of the apothem in that line; what is a?
 
HallsofIvy said:
In your second line, you say that "a stands for apothem" (You mean that a stands for the length of the apothem- let's be precise!) but in the third line you say "apothem: square root of a times square root of three". Obviously a is not the length of the apothem in that line; what is a?
My answer was wrong.:confused: I'm guessing there's another method to solve this, like plugging in numbers... Instead of making X the unknown value, i used "a" .
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

The radio of a triangle inside circle
Replies
4
Views
8K
How can I solve two challenging GRE math problems without a calculator?
Replies
6
Views
3K
Solving Geometry Problems involving Fractions and Triangles
Replies
16
Views
2K
Geometry & Trigonometry - Two solutions
Replies
20
Views
2K
Curiosity about infinity in geometry(Not homework just curious)
Replies
2
Views
2K
Geometry - calculating a distance
Replies
3
Views
2K
Did the Math Department get this wrong?
Replies
5
Views
2K
I Doubling a Cube: Can 3D Geometry Help?
Replies
4
Views
2K
How to solve a geometry problem involving concentric rectangles?
Replies
8
Views
3K
B Confused about dot product multiplication
Replies
33
Views
4K

Hot Threads

Recent Insights

Back
Top