Suppose you want to build a fence around a rectangular enclosure and have 200 yards of material to use.

Question

In addition, suppose there is a long brick wall you can use for one of the

sides. Let x denote the length (in yards) of the sides perpendicular to the brick wall.

(a) Write the formula for A(x), the area (in square yards) of the rectangular enclosure

surrounded by the fencing, and use Python to expand it.

(b) What is the area when the sides perpendicular to the wall are 20 yards long each?

(c) How long does each side perpendicular to the wall need to be to achieve an enclosed area

of 4200 square yards? List all solutions if there is more than one.

Answer 1

If each of the sides perpendicular to the brick wall has length x, then the length of the side parallel to the brick wall is 200 - 2x.

A(x) = x(200 - 2x) = -2x² + 200x

b. A(20) = ?

c. -2x² + 200x = 4200

x² - 100x + 2100 = 0

(x - 30)(x - 70) = 0 So, x = 30 yd or 70 yd.