A rancher wants to build a rectangular pen with an area of 180 . Let W be the width of the pen and L be the length of the pen.

a) Find an equation for the perimeter P in terms of W and L .

b) Use the given area to write an equation that relates W and L .

c) Find the pen dimensions that require the minimum amount of fencing.
Width =
Length =

I need the answer urgent! Thank you. Please provide an explanation on how you did it!

1 answer

P=2(W+L)
A=WL, so L = 180/W

so,

P = 2(W+180/W)

This is pre-cal, so you don't have calculus at your disposal. But, you do know that a square has maximum area for a given perimeter. So,
W = L = √180 = 6√5