Question

Find the dimensions of a rectangle with area 2500 m^2 whose perimeter is as small as possible. List the dimensions in non-decreasing order.

Answer 1

i got x value to be sqrt(1250) and y value to be 2500/sqrt(1250)

Answer 2

Is this calc 3? or calc 1?

Answer 3

\[
A=lw=2500\implies l=2500/w
\]So \[
P=2w+2(2500/w)= 2w+5000/w
\]We take derivative\[
P'=2+\frac{-5000}{w^2}
\]To minimize, it must be 0, so \[
0=2-5000/w^2\implies -2=-5000/w^2\implies w^2=\frac{-2}{-5000}
\]

Answer 4

So, based on what I'm getting. It looks like your answer is correct.

Answer 5

By the way \[
\sqrt{2500}=\sqrt{25\cdot 100}=\sqrt{25}\cdot \sqrt{100}=5\cdot 10=50
\]

Answer 6

So you should have x=50, and y=2500/50=50

Answer 7

I guess the only way to minimize a rectangle's perimeter is to make it a square.