Solve the problem.
-A picture 9 inches by 20 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the mounted
Picture is 476 square inches?
A)4 in.
B)6 in.
C)6.5 in.
D)5 in.

Question

Quizplus · Accepted Answer

The area of the picture is 9 * 20 = 180 square inches. The area of the mounted picture is 476 square inches, so the area of the mat alone is 476 - 180 = 296 square inches. Let x be the width of the border. The dimensions of the mounted picture are (9+2x) by (20+2x). The equation for the area of the mounted picture is (9+2x)(20+2x) = 476. Simplifying, we get 180 + 58x + 4x^2 = 476, which simplifies to 4x^2 + 58x - 296 = 0. Solving this quadratic equation for x gives x = 4 inches as the width of the border.

Solve the Problem. -A Picture 9 Inches by 20 Inches Is to Be