Question

A Square yellow rug has a red square in the center. The side length of the red square is X inches. The width of the yellow band that's surrounds the red square is 6 inches. What is the area of the yellow band?

Answer 1

Answer: The area of yellow band is $24x+144$ sq. inches.

Step-by-step explanation:

Let the side length of the red square be 'x' inches

Width of the yellow band surrounds the red square = 6 inches

So, Length of  band would be

$6+x+6=x+12$

Width of  band would be

$6+x+6=x+12$

So, Area of the yellow band would be

$\text{Area of whole band}-\text{Area of red square}\\\\=(x+12)\times (x+12)-x^2\\\\=(x+12)^2-x^2\\\\=x^2+144+24x-x^2\\\\=24x+144$

Hence, the area of yellow band is $24x+144$ sq. inches.