Question

Miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album. The area of the reduced photo is 64 square inches. In the equation (x – 3)2 = 64, x represents the side measure of the original photo.

What were the dimensions of the original photo?

A. 11 inches by 11 inches
B. 5 inches by 5 inches
C. 3 + 4 StartRoot 2 EndRoot inches by 3 + 4 StartRoot 2 EndRoot inches
D. 3 4 StartRoot 2 EndRoot inches by 3 4 StartRoot 2 EndRoot inches

Answer 1

Answer: Solving the quadratic equation, the dimensions of the original photo are 11 inches by 11 inches.

First option 11 inches by 11 inches

Solution:

Side measure of the original photo: x

(x-3)^2=64

Solving for x: Square root both sides of the equation:

√[(x-3)^2]=±√64

x-3=±8

Adding 3 both sides of the equation:

x-3+3=±8+3

x=±8+3

x1=-8+3→x1=-5<0 (negative), it's not a solution because the side measure of the original photo can be a negative number.

x2=8+3→x2=11>0 (positive). Ok

The solution is x=11 inches(A)

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