Question

A square purple rug has a orange square in the center. The side length of the orange square is x inches. The width of the purple band that surrounds the orange square is 10 in. What is the area of the purple ​band?

Answer 1

`40(x+10)$ square inches`

Explanation:

• Side length of the Orange Square =x inches

Width of the purple band that surrounds the orange square = 10 in.

Since the orange square is in the middle

From the diagram:

• Side Length of the Purple Rug =(x+20) Inches

Therefore:

Area of the Purple Band =Area of Purple Rug -Area of Orange Square

`=(x+20)^2-x^2\\`

`=(x+20)(x+20)-x^2\\=x^2+20x+20x+400-x^2\\=40x+400\\=40(x+10)$ square inches`