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zheka24 [161]
3 years ago
8

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
Mathematics
2 answers:
andreev551 [17]3 years ago
6 0

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:

<u>Side length of blue square = </u>x<u />

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} \\

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

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.

Download docx
Musya8 [376]3 years ago
6 0

Answer is

32x-256

most people put the wrong answer

Step-by-step explanation:

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