Math Perimeter Word Problem

Question

A farmer needs to have 2 000 000 m2 to grow his crops. He is trying to save money on the materials

needed to build a fence around the perimeter of his field. The field borders a river, so he only needs to put

the fence around 3 sides of his property.

a) What dimensions should he use to optimize the perimeter?

b) If the wire for the fencing costs $2.00/m, how much will it cost the farmer to purchase the wire?

Answer 1

2 million = Lw

L=2/w

Fence = L+2w=2/w+ 2w

F'= -2/w^2 +2=0

w^2=1

w=sqr(1 million) meters= fence perpendicular to the river

w= 1,000 meters

L= 2,000 meters parallel to the river