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 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?
A) 2.2 ft
B) 1.5 ft
C) 3 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. However, without solving the quadratic equation directly, we can find the width of the border by understanding that the total area of the border is the difference between the area of the room and the area of the rug. The border is uniform, so it subtracts an equal amount of space from both the length and the width of the room. Given the dimensions and the area of the rug, we can calculate the width of the border directly. The correct width of the border that satisfies the given conditions is 1.5 ft, which is found by recognizing that the border reduces the length and width of the room equally and the area of the rug is consistent with a border of this width around it.

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