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

Question

3 years ago

8

that surrounds the blue square is 6 inches. what is the area of the green band

2 answers:

andreev551 [17] · Answer 1 · 2022-06-11T13:45:35+03:00

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.

Musya8 [376] · Answer 2 · 2022-06-11T16:06:31+03:00

6 0

Answer is

32x-256

most people put the wrong answer

Step-by-step explanation: