Question

A rectangle has a length that is twice the width. The width is to be extended by 5 ft and the length by 3 ft, so the total area becomes 99 square feet. What was the original length?

Answer Choices:
4 ft
6 ft
8 ft
10 ft
12 ft
14 ft
16 ft

Answer 1

8 feet

Explanation:

w = width

2s = length

Find 'w' by multiplying the new dimensions:

(w+5)(2w+3) = 2w² + 3w + 10w + 15 = 99

simplify:

2w² + 13w - 84 = 0

Factor:

(2w + 21)(w - 4) = 0

w = -21/2 ** disregard because a measurement cannot be negative **

w = 4

original width was 4

orginal length was twice 4 or 8 feet