Question

Alex is building a rectangular fence around his yard. The total perimeter of the fence is 68 feet and the area of the yard is 240 square feet. Based on this information, what are the dimensions of the fence?

Answer 1

Perimeter (P) = 2L + 2w

68 = 2L + 2w

68 - 2L = 2w

2(34 - L) = 2(w)

34 - L = w

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Area (A) = L * w

240 = L (34 - L)

240 = 34L - L²

L² - 34L + 240 = 0

(L - 10)(L - 24) = 0

L = 10 or L = 24

w = 34 - L = 34 - 10 = 24 or w = 34 - 24 = 10

Answer: width = 10, length = 24 assuming length is bigger than the width

Answer 2

Perimeter (P) = 2L + 2w

68 = 2L + 2w

68 - 2L = 2w

2(34 - L) = 2(w)

34 - L = w

********************

Area (A) = L * w

240 = L (34 - L)

240 = 34L - L²

L² - 34L + 240 = 0

(L - 10)(L - 24) = 0

L = 10 or L = 24

w = 34 - L = 34 - 10 = 24 or w = 34 - 24 = 10

Answer: width = 10, length = 24 assuming length is bigger than the width