The length of a rectangle is 3 ft less than twice the width. If the total area of the rectangle is 35 ft2, find the width (in ft) of the rectangle.

Answer 1

The area of the rectangle is 35 ft². The length is 2x - 3 with x being the width.

A = lw → x(2x - 3) = 35

2x² - 3x = 35

2x² - 3x - 35 = 0

We can factor this by grouping. Write out the pair of factor groups that multiples to -70 and adds up to -3. Only one pair will work: -10 and +7.

Split the middle term like this: 2x² - 10x + 7x - 35 = 0

2x(x - 5) + 7(x - 5) = 0

(2x + 7)(x - 5) = 0

2x + 7 = 0 → 2x = -7 → x = -3.5 (No negative numbers exist in measurements)

x - 5 = 0 → x = 5

The width of the rectangle is 5 feet.