This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Okay, let's tackle this problem. Step 1: Define variables and set up the perimeter equation. Let the length of the side with the stone wall be x yards. Let the other dimension (width) of the rectangular enclosure be W yards. The fencing is used on the remaining three sides: the two sides of length W and one side of length x. The total length of fencing used is 100 yards. So, the equation for the total fencing is: 2W + x = 100 Step 2: Express W in terms of x. From the fencing equation, we can isolate W: 2W = 100 - x W = (100 - x)/(2) Step 3: Write the formula for the area of the enclosure. The area A of a rectangular enclosure is given by the product of its length and width. In this case, the dimensions are x and W. A = x · W Step 4: Substitute the expression for W into the area formula. Substitute W = (100 - x)/(2) into the area formula to express A as a function of x: A(x) = x ( (100 - x)/(2) ) A(x) = (100x - x^2)/(2) A(x) = 50x - (1)/(2)x^2 The area of the enclosure as a function of x is: A(x) = 50x - (1)/(2)x^2 3 done, 2 left today. You're making progress.