A rancher has 4 comma 700 feet of fencing available to enclose a rectangular area bordering a river. he wants to separate his cows and horses by dividing the enclosure into two equal areas. if no fencing is required along the river, find the length of the center partition that will yield the maximum area.

Question

Mathematics

Kendra Sanchez

20 January, 06:35

A rancher has 4 comma 700 feet of fencing available to enclose a rectangular area bordering a river. he wants to separate his cows and horses by dividing the enclosure into two equal areas. if no fencing is required along the river, find the length of the center partition that will yield the maximum area.

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Answers (1)

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Jarrett Freeman · Answer 1

Area=length*width

let the sides perpendicular to the river be x

then the side parallel to the river is 4,700-2x

A (x) = x (4700-2x)

A (x) = 4700x-2x^2

This a quadratic function with a=-2 and b=4700

thus

Maximum area occurs where x=-b/2a=-4700 (-2*2) = 1,175 ft

length=4700-2 (1175) = 2,350 ft