Jack and Jill have purchases a new puppy and need to fence in a rectangular dog

Question

Jack and Jill have purchases a new puppy and need to fence in a rectangular dog run in their back yard. What is the maximum are they can enclose with 420 feet of fencing if they use the house for one of the sides? ( So they only need fencing on three of the sides) Jack and Jill have purchases a new puppy and need to fence in a rectangular dog run in their back yard. What is the maximum are they can enclose with 420 feet of fencing if they use the house for one of the sides? ( So they only need fencing on three of the sides)

Explanation / Answer

Fencing is 2 sides of equal length(x) + one side with length of house's side(y) 2x + y = 420 y = 420 - 2x Area(x) = xy = x(420 - 2x) = 420x - 2x^2 Maximum area = Area(x) when x = -b/2a = -420/-4 = 105 420(105) - (105)^2 = 44100 - 22050 = 22050 ft^2

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