Question

A square purple rug has a orange square in the center. The side length of the orange square is x inches. The width of the purple band that surrounds the orange square is 12 in. What is the area of the purple band?

Answer 1

578 + 48 square inches

Explanation:

The computation of the area of the purple band is as follows:

Area of the green square = side^2 = x^ square inches

And, the area of the orange square = side^2

The side would be = = 12 + 12 +x = 24 + x

And, now the area would be = (x + 24)^2

Now the area of the orange band is

= Area of the orange square area of the green square

= (x + 24)^2 - x^2

= x^2 + 24^2 + 48 - x^2

= 578 + 48 square inches