shayna enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster. the…

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? 4 inches by 4 inches 6 inches by 6 inches 10 inches by 10 inches 12 inches by 12 inches

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? 4 inches by 4 inches 6 inches by 6 inches 10 inches by 10 inches 12 inches by 12 inches

Answer

Explanation:

Step1: Take square - root of both sides

Take the square - root of the equation ((x + 10)^2=256). We get (x + 10=\pm\sqrt{256}). Since (\sqrt{256}=16), the equation becomes (x + 10=\pm16).

Step2: Solve for (x) when (x + 10 = 16)

Subtract 10 from both sides of the equation (x+10 = 16). So (x=16 - 10=6).

Step3: Solve for (x) when (x + 10=-16)

Subtract 10 from both sides of the equation (x + 10=-16). So (x=-16 - 10=-26). But since (x) represents the side - length of a square (a non - negative quantity), we discard (x=-26).

Answer:

6 inches by 6 inches