Question

optimization calculus problem help.
Show that among all rectangles with 8-m perimeter, the one that is largest is a square.

Answer 1

let perimeter = 2x + 2y = 8
maximize perimeter (take derivative of it)
set it = 0

Answer 2

the derivative of it would be 2+2=0

Answer 3

do you mean the one that is the largest area?

Answer 4

yeah largest area

Answer 5

if thats what you mean you have to maximize the area equation A = xy

Answer 6

where 2x + 2y = 8, so
2y = 8 - 2x
y = 4 - x

A = x*y
A = x (4 - x)
maximize this one

Answer 7

4-2x=0

Answer 8

x=2

Answer 9

so x = 2 that means the perimeter is

p = 2x + 2y = 8
p = 4 + 2y = 8
solve for y

Answer 10

y=2

Answer 11

perfect!

Answer 12

how would i write the answer?

Answer 13

well the work you showed proved that the value of x when the area is maximized is x = 2
then you solved for y using x = 2, and found y = 2
the dimensions of the rectangle is x by y, or 2 by 2, which is a square

that means to maximize the area, the rectangle has to be a square

Answer 14

thank you so much for your help!