# Quadratic Question Dealing With Perimeter

## 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!

tiny-tim
Homework Helper
hi kylepetten! … 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! hi kylepetten! ok so far … and now you need an expression for the area! SA = x^2 + x^2 + xy + xy + xy + xy
SA = 2x^2 + 4xy

That what you meant?

tiny-tim
Homework Helper
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 )

Yup! So if 2x + y is constant, how do you maximise x2 + 2xy ? (try using the X2 icon just above the Reply box )

Yup! So if 2x + y is constant, how do you maximise x2 + 2xy ? 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.

tiny-tim
Yep, that should do it! Yep, that should do it! Thanks a lot! 