Justin wants to fence three sides of a rectangle exercise yard for his dog. the fourth side of the exercise yard will be a side of the house. he has 56 feet of fencing available. find the dimensions that will maximize the area of the exercise yard. side opposite the house is feet long other two sides are both feet long

Question

Mathematics

Kendal Ortiz

28 February, 15:02

Justin wants to fence three sides of a rectangle exercise yard for his dog. the fourth side of the exercise yard will be a side of the house. he has 56 feet of fencing available. find the dimensions that will maximize the area of the exercise yard. side opposite the house is feet long other two sides are both feet long

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Answers (1)

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Carolyn Stevenson · Answer 1

Set up an equation.

width = x

length = 56 - 2x

Multiplying length * width makes area. 56x - 2x^2 = Area.

y = - 2x^2 + 56x

Ax^2 + Bx = C

Solve for the vertex: x = - (b/2a)

- (56/-4) = 14

width = 14 ft.

length = 56 - 2 (14) = 28ft.

14*28 = 392 sq. ft.