Solve the problem.
-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 15 feet by 21 feet and the area of the rug is 216 square feet, how wide will the border be?
A)1.5 ft
B)4 ft
C)3.5 ft
D)2.5 ft

Question

Quizplus · Accepted Answer

The area of the room is 15 ft * 21 ft = 315 square feet. The area of the rug is 216 square feet, so the area of the border is 315 - 216 = 99 square feet. Let x be the width of the border. The dimensions of the rug will then be (15 - 2x) by (21 - 2x), and the area of the rug is (15 - 2x)(21 - 2x) = 216. Simplifying, we get 315 - 72x + 4x^2 = 216, which simplifies to 4x^2 - 72x + 99 = 0. Solving for x gives x = 1.5 ft, which means the border is 1.5 feet wide.

Solve the Problem. -A Rug Is to Fit in a Room So That