Solve the problem.
-A picture is to be mounted on a piece of matte board 12 inches by 20 inches so that there is an even amount of matting all around the picture. How wide will the border be if the area of the mounted picture is 420 square inches?
A) 5 in.
B) 6 in.
C) 7.5 in.
D) 7 in.

Question

Quizplus · Accepted Answer

The area of the mounted picture is 420 square inches, so the area of the picture is 420 - (12 x 20) = 120 square inches. The width of the border is (12 - 2x) / 2 = 6 - x, and the height of the border is (20 - 2x) / 2 = 10 - x. The area of the border is (6 - x)(10 - x) = 60 - 16x + x^2. Setting this equal to 120 and solving for x gives x = 5.

Solve the Problem. -A Picture Is to Be Mounted on a Piece of a Piece