Question

mitam 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?

• 11 inches by 11 inches
• 5 inches by 5 inches
• (3 + 4sqrt{2}) inches by (3 + 4sqrt{2}) inches
• (3 - 4sqrt{2}) inches by (3 - 4sqrt{2}) inches

Explanation:

Step1: Solve the equation \((x - 3)^2 = 64\)

Take the square root of both sides: \(x - 3=\pm\sqrt{64}\)
Since \(\sqrt{64} = 8\), we have \(x - 3=\pm8\)

Step2: Solve for \(x\) in two cases

Case 1: \(x - 3 = 8\)
Add 3 to both sides: \(x=8 + 3=11\)

Case 2: \(x - 3=-8\)
Add 3 to both sides: \(x=-8 + 3=-5\)
But the side length of a photo can't be negative, so we discard \(x = - 5\)

So the side length of the original square photo is 11 inches, so the dimensions are 11 inches by 11 inches.

Answer:

A. 11 inches by 11 inches