Three sides of a fence and an existing wall form a rectangular enclosure. The total length of a fence used for the three sides is 240 feet. Let x be the length of two sides perpendicular to the wall. Write an equation of area A of the enclosure as a function of x for the rectangular area for which the area is 5500 ft.

Question

Cyrus

Mathematics

6 August, 14:12

Three sides of a fence and an existing wall form a rectangular enclosure. The total length of a fence used for the three sides is 240 feet. Let x be the length of two sides perpendicular to the wall. Write an equation of area A of the enclosure as a function of x for the rectangular area for which the area is 5500 ft.

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Answers (1)

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Alina Howell · Answer 1

A (x) = x (240 - 2x) 5500 = - 2x² + 240x

Step-by-step explanation:

One of the dimensions of the rectangular space is x, as given in the problem statement. The amount of fence available for the other dimension of the rectangle is (240 - 2x). So, the area is ...

A (x) = x (240 - 2x)

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When the area is 5500 ft², the equation is ...

5500 = x (240 - 2x)

5500 = - 2x² + 240x