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 17 feet by 22 feet and the area of the rug is 204 square feet, how wide will the border be?
A) 5 feet
B) 2.5 feet
C) 4.5 feet
D) 3.5 feet

Question

Quizplus · Accepted Answer

The area of the room is 17 * 22 = 374 square feet. The area of the rug is 204 square feet, so the area of the border is 374 - 204 = 170 square feet. Let x be the width of the border. The dimensions of the rug will then be (17 - 2x) by (22 - 2x). The area of the rug is also given by the equation (17 - 2x)(22 - 2x) = 204. Simplifying this equation gives a quadratic equation in terms of x. Solving for x, we find that x = 2.5 feet.

A Rug Is to Fit in a Room So That