Question

a square red rug has a purple square in the center. the side length of the purple square is x inches. the width of the red band that surrounds the purple square is 5 in. what is the area of the red band

Answer 1

Answer:

Area of red band is $(20x + 100) inch^{2}$

Step-by-step explanation:

We know that area of square = $side^{2}$

Please refer to the attached figure, we have to calculate the area of red band.

Required area = Area of square ABCD - Area of purple square

Side of purple square = $x$

So, area of purple square = $x^{2}$

ABCD is a square with purple square at the center and there is symmetry in the figure.

So, width of red band towards both the end is 5 inches.

$\Rightarrow \text{side of }ABCD = 5 + 5 +x = (x+10) inches$

Required area = $(x+10)^{2} - x^{2}$

Using formula $a^{2} - b^{2} = (a-b)\times (a+b)$

$\Rightarrow (x+10-x)(x+10+x)\\\Rightarrow (10)(2x+10)\\\Rightarrow (20x+100)$

Hence, Area of red band is $(20x + 100) inch^{2}$