Question

Stefon is painting the ceiling of a room. The ceiling is in the shape of a rectangle. He has enough paint to cover 180 square feet. The length of the ceiling is 11 feet longer than its width. What are the dimensions of the ceiling?

A. l = 29 ft; w = 18 ft
B. l = 21 ft; w = 10 ft
C. l = 26 ft; w = 15 ft
D. l = 20 ft; w = 9 ft

Answer 1

D. l = 20 ft; w = 9 ft

Explanation:

The area of a rectangle is width times length:

180 = WL

We're told the length is 11 feet longer than the width:

L = W + 11

Substituting:

180 = W (W + 11)

180 = W² + 11W

0 = W² + 11W − 180

0 = (W + 20) (W − 9)

W = -20, 9

Since W can't be negative, W = 9.

L = W + 11

L = 20

Hint: on a timed multiple choice test, like the SAT or ACT, it's sometimes faster to check each answer rather than do the math. We know the area is 180, so simply multiply each length and width and see which is right:

A. 29 ft × 18 ft = 522 ft²

B. 21 ft × 10 ft = 210 ft²

C. 26 ft × 15 ft = 390 ft²

D. 20 ft × 9 ft = 180 ft²