A total of x feet of fencing is to form three sides of a level rectangular yard. What is the maximum possible area of the yards in terms of x?
- x²/4
- x²/6
- x²/8
- None of these
Explanation
Let width = W, length = L. Fence for 3 sides: L + 2W = x → L = x - 2W
Area A = L×W = (x - 2W)W = xW - 2W²
For max, dA/dW = x - 4W = 0 → W = x/4
Then L = x - 2(x/4) = x/2
Max area = L×W = (x/2)(x/4) = x²/8
Last verified on 05-06-2026
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