Question

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

Answer 1

Answer:

the area of Green band is $576+48x \ in^2$.

Step-by-step explanation:

Given:

side length of yellow square = x in

Length of the green square = $12+x+12 =24+x \ in$

We need to find the area of the green band.

Solution:

First we will find the area of Yellow square.

area of Yellow square is equal to square of the side length.

framing in equation form we get;

area of Yellow square = $x^2\ in^2$

Area of the whole square = $(24+x)^2 = 576+48x+x^2$

Now to find the area of the green square we will subtract area of Yellow square from Area of the whole square.

framing in equation form we get;

area of the green square = $576+48x+x^2-x^2 =576+48x$

Hence the area of Green band is $576+48x \ in^2$.