SOLUTION: A man has a swimming pool in the form of a square. He constructs a cement walk 6 feet wide around the pool and finds that the area of the walk is exactly 1/2 the area of the pool.
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Question 184158: A man has a swimming pool in the form of a square. He constructs a cement walk 6 feet wide around the pool and finds that the area of the walk is exactly 1/2 the area of the pool. What is the length of the pool? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A man has a swimming pool in the form of a square. He constructs a cement walk 6 feet wide around the pool and finds that the area of the walk is exactly 1/2 the area of the pool. What is the length of the pool?
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Draw the picture of a rectangle inside a rectangle.
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Let dimensions of the inner rectangle be L and W
Area of the inner rectangle is then L*W
This is the area of the pool.
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The dimensions of the outer rectangle are L+12 and W+12
Area of the outer rectangle is (L+12)*(W+12)
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Equation:
Area of the walk = outer area - inner area
= (LW+12L + 12W + 144) - LW = 12L + 12W + 144
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Equation:
Area of walk = (1/2) area of pool
12L + 12W + 144 = (1/2)LW
24L + 24W + 288 = LW
LW - 24L = 24W + 288
L(W-24) = 24W + 288
Length = (24W+288)/(W-24)
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Cheers,
Stan H.
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