A total of x feet of fencing is to form three sides of a rectangular yard. What is the maximum possible area of the yard in terms of x?

Let's denote the length of the yard as l and the width as w. Since only three sides are fenced, we can express the total length of the fencing as:

    
• l + 2w = x

From this equation, we can express l in terms of w:

    
• l = x - 2w

The area A of the rectangle is given by:

    
• A = l * w = (x - 2w) * w = xw - 2w^2

To maximize the area, we can take the derivative of A with respect to w, set it to zero, and solve for w. This leads to the maximum area being when w = x/4 and substituting back to find l gives l = x/2.

Substituting these values into the area formula yields:

    
• A = (x/2)(x/4) = x^2/8

Thus, the maximum possible area of the yard in terms of x is $\frac{x^2}{8}$, which corresponds to option c, confirming that the given answer is indeed correct.

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