Question

A new homeowner needs to put up a fence to make his yard secure. the house itself forms the south boundary and the garage forms the west boundary of the property, so he needs to fence only 2 sides. the area of the yard is 4000 sq ft. he has enough material for 160 ft of fence. find the length and width of the yard.

Answer 1

Let the width = x feet, then the length = 160 - x  feet.

The area =  x * (160 - x) = 4000

160x - x^2 = 4000

x^2 - 160x + 4000 = 0

x =  [- (-160) +/-  sqrt (160^2 - 3 * 1 * 4000)] / 2

x =   128.98 or 31.01

answer is length = 129 feet and width = 31 feet   ( to nearest foot).