Question

A rug is to fit in a room so that a border of even width is left on all four side. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet how wide will the border be

Answer 1

(12 - 2x)(15 - 2x) = 108

180 - 24x - 30x + 4x² = 108

180 - 54x + 4x² = 108

4x² - 54x + 72 = 0

2x² - 27x + 36 = 0

(2x - 3)(x - 12) = 0

2x - 3 = 0 x - 12 = 0

x = 3/2 x = 12

Since the length of the border must be less than the width, disregard the 12

x = 3/2 = 1.5

Answer: 1.5 ft