Question

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

Answer 1

The area of the orange ​band is 576 + 48x square inches

Explanation:

Step 1: Area of the green square

The area of the green square =
`side^2`

The area of the green square =
`x^2` square inches

Step 2: Area of the orange square

The area of the orange square =
`side^2`

The side of the orange square = 12+12 + x = 24 +x

Now the area of the orange square =
`(x+24)^2`

Step 3: The area of the orange ​band

Area of the orange ​band = area of the orange square - area of the green square

Area of the orange ​band =
`(x+24)^2 - x^2`

expanding and solving the equation we get

`x^2 + 24^2 +48x - x^2`

`576 + 48 x` square inches