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.

Question

Mathematics

Winston Kennedy

28 November, 00:33

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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Answers (1)

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Joshua Howell · 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).