A square purple rug has a blue square in the center. The side length of the blue square is x inches and the purple region is 8 in. What is the area of the purple part.

(x+8)^2 - x^2

answer

16

To find the area of the purple part, we need to subtract the area of the blue square from the total area of the purple rug.

We know that the side length of the blue square is x inches. So, the area of the blue square is x * x = x^2 square inches.

The side length of the purple rug can be found by adding twice the side length of the blue square (for the top and bottom sides) to the side length of the blue square. Therefore, the side length of the purple rug is 2x + x = 3x inches.

The total area of the purple rug is then (3x) * (3x) = 9x^2 square inches.

Since the purple region is 8 square inches, we can subtract the area of the blue square from the total area of the purple rug to find the area of the purple part: 9x^2 - 8 square inches.