Question

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?

A. 8 inches by 8 inches
B. 9 inches by 9 inches
C. 12 inches by 12 inches
D. 13 inches by 13 inches

Answer 1

B. 9 inches by 9 inches

Explanation:

he formula for the area of a square is length x width

For a square the length and the width are same therefore it is

length x length = (length)² (let’s call this first equation)

also (x + 2 )²= 121 (let’s call this second equation)

To form an equation for the cropped picture from the original picture

Length = (cut off length + new length) (third equation)

Length = ( 2 + x) fourth equation

assuming the new lenght is x

Since 2 is the cut off length from each sides

Lets substitute first equation into second equation then we will have

Lenght² = 121

Length = √121

Length = 11

Substitute into fourth equation

Length = 11 = (x+2)

X+2 =11

X= 11 - 2

X=9

Answer 2

Answer: B. 9 inches by 9 inches

x = -13 or x = 9

x cannot be negative, so

x = 9 inches

Therefore, the dimensions of the cropped photo is 9 inches by 9 inches.

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?

A. 8 inches by 8 inches

B. 9 inches by 9 inches

C. 12 inches by 12 inches

D. 13 inches by 13 inches

Explanation:

Given that;

(x+2)^2 = 121. ....1

x = size of cropped picture.

To solve for x,

From eqn1

x^2 + 4x + 4 = 121

x^2 + 4x - 117 = 0

Solving the quadratic equation gives;

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

x = -13 or x = 9

x cannot be negative, so

x = 9 inches

Therefore, the dimensions of the cropped photo is 9 inches by 9 inches.