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

Answer:

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

Step-by-step 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