Question

shayna enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster. the area of the enlarged photo is 256 square inches. in the equation ((x + 10)^2 = 256), (x) represents the side measure of the original square photo. what were the dimensions of the original photo? 10 inches by 10 inches 4 inches by 4 inches 12 inches by 12 inches 6 inches by 6 inches

Explanation:

Step1: Solve the equation \((x + 10)^2 = 256\)

Take the square root of both sides: \(x + 10=\pm\sqrt{256}\)
Since \(\sqrt{256} = 16\), we have \(x + 10=\pm16\)

Step2: Consider the positive solution (side length can't be negative)

Case 1: \(x + 10 = 16\)
Subtract 10 from both sides: \(x=16 - 10 = 6\)

Case 2: \(x + 10=-16\)
Subtract 10 from both sides: \(x=-16 - 10=-26\) (discarded as side length can't be negative)

So the side length of the original square photo is 6 inches, so the dimensions are 6 inches by 6 inches.

Answer:

6 inches by 6 inches