Solve.
-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 10 feet by 16 feet and the area of the rug is 72 square feet, how wide will the border be?
A)4.5 ft
B)4 ft
C)3 ft
D)2 ft

Question

Quizplus · Accepted Answer

Let the width of the border be "x" feet. Then the dimensions of the rug are (10-2x) feet by (16-2x) feet.

The area of the rug is given as 72 square feet, so we can write:
(10-2x)(16-2x) = 72

Expanding the left side and simplifying, we get:
4x^2 - 52x + 128 = 0

Factoring, we get:
(2x-8)(2x-16) = 0

So, either 2x-8 = 0 or 2x-16 = 0. Solving for x in each case, we get:
x = 4 or x = 8/2

Since the width of the border must be even, x = 4 is the only possible value. Therefore, the width of the border will be 4 feet.

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