Question

Four hundred yards of fence is to be used to endose 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 ofthe rectangle. Suppose the width w in yards of the rectangle is along the river bank.(a) Express the height of the rectangle in terms of w.b) Express the area of the rectangle in terms of w.

Answer 1

400 yards of fence = total fencing

400 = 2 widths + 2 heights

Since one side (width) is along the river, and the river bank acts as one side of the rectangle, the fence will be used in 3 sides:

400 = w+2h

Solving for h:

400-w=2h

(400-w)/2 = h

h= (400-w)/2 (a)

h= 200-1/2w (simplified)

To express the area:

Area of a rectangle : height x width

Since h = 200-1/2w

A = (200-1/2w) w

A = 200w-1/2w^2 (b)