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.

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Mathematics

14 October, 11:04

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.

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Zackary · 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).