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.

Question

anonymous · Answer

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

anonymous · Answer

Is this calc 3?  or calc 1?

anonymous · Answer

$$
A=lw=2500\implies l=2500/w
$$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 $$
0=2-5000/w^2\implies -2=-5000/w^2\implies w^2=\frac{-2}{-5000}
$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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