Find the length and width

Question

A farmer wants to fence a rectangular area of 50 sq ft next to a river . Find the length and width . Assuming the length is parallel to the river.

Answer 1

L= 50/W. LW=50=Area

50/W + 2W= P = Perimeter = Total fencing needed

take the derivative and set equal to zero

P' =2 -50/W^2 =0

2W^2 -50 =0

W= +/-5

W=5 feet wide, ignore negative solution

L=50/W =50/5 = 10 feet long

for the minimum fencing needed