Question

a square green rug has a blue square in the center. the side length of the blue square is x inches. the width of the green band that surrounds the blue square is 6 inches. what is the area of the green band

Answer 1

Answer:

$12(x+3)$ square inches.

Step-by-step explanation:

Given:

A square green rug has a blue square in the center.

The side length of the blue square is x inches as shown in the figure:

The width of the green band that surrounds the blue square is 6 inches.

Question asked:

What is the area of the green band ?

Solution:

Side length of blue square = $x$

First of all we will calculate area of blue square.

As we know:

$Area of square=(Side)^{2}$

                       $=x^{2}$

Thus, area of blue square = $x^{2}$

Now, we will calculate area of square green rug:

Side length of green rug = Side length of blue square + width which surrounds the blue square

Side length of green rug = $x+6$

Thus,  area of square green rug = $=(x+6)^{2}$

Now, we will find area of the green band ( shaded region with green color as shown in the figure)

Area of the green band = Area of square green rug -  Area of blue square        

                                       $=(x+6)^{2} -x^{2} \\=(x+6+x)(x+6-x)\ [a^{2} -b^{2} =(a+b)(a-b)]$

                                       $=(2x+6)6\\=12x+36$

                                       $=12(x+3)\ taking\ 12\ as\ common$

Therefore, the area of the green band is $12(x+3)$ square inches.