Question

A square rug has an inner square in the center. The side length of the inner square is x inches, and the width of the outer region is 3 in. What is the area of the outer part of the​ rug?

Answer 1

`12x+36` in²

Explanation:

The area of the inner square is
`x^2` in².

The area of the whole square is
`(x+6)^2` in².

Taking the difference,
`(x+6)^2-x^2=(6)(2x+6)=12x+36` in².

Answer 2

`\huge\boxed{\sf 12x + 36 \ in.^2}`

Explanation:

Formula:

• Area of square = length²

Area of inner part of the rug:

Length = x in.

So,

Area = (x)²

Area = x² in.²

Area of the whole rug:

Length of the whole rug = 3 + x + 3 = x + 6

So,

Area = (x + 6)²

Area = x² + 12x + 36 in.²

Area of the outer part of the rug:

= Area of the whole rug - Area of the inner part

= x² + 12x + 36 - x²

= x² - x² + 12x + 36

= 12x + 36 in.²

`\rule[225]{225}{2}`