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 12 in. what is the area of the outer part of the rug? (simplify your answer)

Explanation:

Step1: Find side - length of outer square

The side - length of the outer square is $x + 12+12=x + 24$ inches.

Step2: Find area of outer square

The area formula for a square is $A = s^2$, where $s$ is the side - length. So the area of the outer square $A_{outer}=(x + 24)^2=x^{2}+48x + 576$ square inches.

Step3: Find area of inner square

The side - length of the inner square is $x$ inches, so the area of the inner square $A_{inner}=x^{2}$ square inches.

Step4: Find area of outer part

The area of the outer part of the rug $A = A_{outer}-A_{inner}$. Substitute the expressions for $A_{outer}$ and $A_{inner}$: $A=(x^{2}+48x + 576)-x^{2}=48x + 576$ square inches.

Answer:

$48x + 576$