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
