A rug is to fit in a room so that a border of even width is left on all four sides. 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?
A) 1.5 ft
B) 3 ft
C) 2.2 ft
D) 1 ft

Question

Quizplus · Accepted Answer

The area of the room is 12 ft * 15 ft = 180 square feet. The area of the rug is 108 square feet, so the area of the border is 180 - 108 = 72 square feet. Let x be the width of the border. The dimensions of the rug will then be (12 - 2x) by (15 - 2x). The area of the rug is also given by the equation (12 - 2x)(15 - 2x) = 108. Simplifying this equation gives a quadratic equation in terms of x. Solving for x, we find that x = 1.5 feet, meaning the border is 1.5 feet wide.

A Rug Is to Fit in a Room So That