Question 338584: the perimeter of a large rectangular store room measures 900 ft. the surface area of its floor is found to be 50,000 sq ft. how long is each side of the room?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! the perimeter of a large rectangular store room measures 900 ft. the surface area of its floor is found to be 50,000 sq ft. how long is each side of the room?
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Let x = width
and y = length
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From: "the perimeter of a large rectangular store room measures 900 ft." we get
2(x+y) = 900 (equation 1)
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From: "surface area of its floor is found to be 50,000 sq ft" we get
xy = 50000 (equation 2)
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Solve equation 2 for y:
y = 50000/x
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Substitute above into equation 1 and solve for x:
2(x+y) = 900
2(x+50000/x) = 900
multiplying both sides by x:
2(x^2 + 50000) = 900x
x^2 + 50000 = 450x
x^2 - 450x + 50000 = 0
factoring the left:
(x-250)(x-200) = 0
x = {250, 200}
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lengths of each side then are
250 feet and 200 feet
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