For what values of m does Liliana decides to crop a square photo 2 inches on each side to fit it into a frame. The area of the original photo was 121 square inches. In the equation (x + 2)2 = 121, x represents the side measure of the cropped photo.

What are the dimensions of the cropped photo?

8 inches by 8 inches
9 inches by 9 inches
12 inches by 12 inches
13 inches by 13 inches

9 inches by 9 inches

Step-by-step explanation:

(x+2)² = 121

We have to solve for x as,

x² +4x + 4 = 121

x² + 4x = 121 - 4

x² + 4x = 117

x²+ 4x - 117 = 0

Sum = coeffient of x = 4

Product = constant = -117

Now we have to find 2 numbers which satisfies the above 2 conditions are 13 and -9.

13 - 9 = 4

13 × -9 = -117

x² + 13x - 9x -117 = 0

Taking common factors as,

x(x+13) -9(x+13) = 0

(x-9)(x+13) = 0

x-9 = 0 or x + 13 = 0

x = 9 or x = -13

The side measure cannot be negative(-13), so x = 9 is the solution.

So the dimension of the cropped photo is 9 inches by 9 inches.