Question

Five hundred yards of fence is to be used to enclose a rectangular area next to a straight river. The river bank acts as one side of the rectangle, and the fence is used to make the other three sides of the rectangle. Suppose the width w in yards of the rectangle is along the river bank.

Answer 1

the requirements are missing:

1. express the height of the rectangle in terms of w
2. express the area of the rectangle in terms of w

1) the height of the rectangle is:

w + h + h + w = 500 + w

2w + 2h = 500 + w

2h = 500 + w - 2w = 500 - w

h = (500 - w) / 2 = 250 - 0.5w

2) the are of the rectangle is:

w x h = w x (250 - 0.5w) = 250w - 0.5w²