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The perimeter of a rectangular cutting board is 48 inches. The area is 135 square inches. What are the dimensions of the cutting board?
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There is a way to solve it MENTALLY.
From the condition, L + W = = 24 inches, and the average of L and W is a = = 12 in.
It is clear that the values L and W are equidistant from "a": L-a = a-W.
Let x = L-a = a-W.
Then L = a + x, W = a-x, or L = 12+x, W = 12-x.
For the area we have LW = 135 = (12+x)*(12-x).
Thus we have an equation for x: = 135, or = 144 - 135 = 9.
Then x = 3. Hence, L = 12+3 = 15 inches and W = 12-3 = 9 inches.
Answer. The length is 15 inches. The width is 9 inches.