A 20-ft by 40-ft swimming pool is surrounded by a deck d feet wide. What is the area of the deck?

4d^2 + 120d

Step-by-step explanation:

There are several ways of solving this problem. This is one of them.

Draw a rectangle and label its length 40 ft and the width 20 ft. Now draw a larger rectangle outside the first rectangle. Keep the distance between the new rectangle and the old rectangle the same on all sides. The distance is d.

The length of the outer rectangle is 40 + 2d. The width of the outer rectangle is 20 + 2d.

Now we find the area of the outer rectangle and subtract from it the area of the inner rectangle. That is the area of the deck.

Outer rectangle: 2d + 40 by 2d + 20

Inner rectangle: 40 by 20

Area of outer rectangle: (2d + 40) (2d + 20)

Area of inner rectangle: 40 (20)

Area of deck:

(2d + 40) (2d + 20) - 40 (20) =

= 4d^2 + 40d + 80d + 800 - 800

= 4d^2 + 120d