Question

A 5 in x 7 in picture is in a frame of uniform width x. The area of the picture and the frame together is 99 in2. How wide is the frame?
A. 1 inch

B. 2 inch

C. 2 1/2 inch

D. 8 inch

Answer 1

Answer: B. 2 inch

Step-by-step explanation:

Let x represent the uniform width of the frame.

The original dimensions of the picture is 5 in x 7 in. This means that the new width of the picture together with the frame is (5 + 2x) in and the new length of the picture together with the frame is (7 + 2x) in.

The formula for determining the area of a rectangle is expressed as

Area = length × width

The area of the picture and the frame together is 99 in2. Therefore,

(5 + 2x)(7 + 2x) = 99

35 + 10x + 14x + 4x² = 99

4x² + 24x + 35 - 99 = 0

4x² + 24x - 64 = 0

Dividing through by 4, it becomes

x² + 6x - 16 = 0

x² + 8x - 2x - 16 = 0

x(x + 8) - 2(x + 8) = 0

x - 2 = 0 or x + 8 = 0

x = 2 or x = - 8

The width cannot be negative. So

x = 2 in

Answer 2

Answer: B.) 2 inches

Step-by-step explanation: