Quadratic Question Dealing With Perimeter

In summary, the conversation discusses finding the dimensions for a rectangular holiday package with a square base that will produce the largest possible surface area. The sum of all the edges of the package is given as 140 cm, and the equation P=8x+4y is used to represent the perimeter. After some calculations, the expression for surface area is determined to be SA = 2x^2 + 4xy. The conversation then discusses how to maximize this expression by using the constant 2x+y and the formula x = -b / 2a.
  • #1
kylepetten
25
0

Homework Statement



Jillian is getting ready to send a holiday package in the mail. The rectangular package has a square base and the sum of all the edges of the package measures 140 cm. What dimensions will produce a package with the largest possible surface area?



Homework Equations



Let x = widths and y = heights



The Attempt at a Solution



P=8x + 4y
140 cm = 8x +4y
-4y = 8x - 140 cm
y = -2 + 35 cm

This is as far as I can get. Am I supposed to solve for x? Please lend me a hint. Thanks a bunch!
 
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  • #2
hi kylepetten! :smile:
kylepetten said:
… What dimensions will produce a package with the largest possible surface area?

P=8x + 4y
140 cm = 8x +4y
-4y = 8x - 140 cm
y = -2 + 35 cm

This is as far as I can get.

ok so far … and now you need an expression for the area! :wink:
 
  • #3
tiny-tim said:
hi kylepetten! :smile:


ok so far … and now you need an expression for the area! :wink:

SA = x^2 + x^2 + xy + xy + xy + xy
SA = 2x^2 + 4xy

That what you meant?
 
  • #4
kylepetten said:
SA = x^2 + x^2 + xy + xy + xy + xy
SA = 2x^2 + 4xy

That what you meant?

(try using the X2 icon just above the Reply box :wink:)

Yup! :biggrin:

So if 2x + y is constant, how do you maximise x2 + 2xy ? :wink:
 
  • #5
tiny-tim said:
(try using the X2 icon just above the Reply box :wink:)

Yup! :biggrin:

So if 2x + y is constant, how do you maximise x2 + 2xy ? :wink:

Am I off track by saying fill in -2x+35 for y?

Then use x = -b / 2a ?

Thanks for all the help, by the way.
 
  • #6
Yep, that should do it! :smile:
 
  • #7
tiny-tim said:
Yep, that should do it! :smile:

Thanks a lot! :approve:
 

1. What is a quadratic equation?

A quadratic equation is a mathematical expression of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is a polynomial equation of degree 2 and can have two possible solutions.

2. How does a quadratic equation relate to perimeter?

In the context of perimeter, a quadratic equation is used to find the dimensions of a rectangle with the largest possible area given a fixed perimeter. This can be achieved by using the quadratic formula to solve for the dimensions.

3. What is the formula for finding the perimeter of a rectangle?

The formula for finding the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. This formula can be used to create a quadratic equation when the perimeter is given and the goal is to find the dimensions with the largest area.

4. Can a quadratic equation be used to find the perimeter if the area is given?

Yes, a quadratic equation can be used to find the perimeter if the area is given. This can be achieved by setting up a quadratic equation in terms of the perimeter and solving for the perimeter using the quadratic formula.

5. How many solutions can a quadratic equation have?

A quadratic equation can have two solutions, one solution, or no real solutions. The number of solutions is determined by the discriminant (b^2 - 4ac) in the quadratic formula. If the discriminant is positive, there are two real solutions. If it is zero, there is one real solution. If it is negative, there are no real solutions.

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