Answer:
the area of the outer part of the rug is 44x + 484 square inches, where x is the side length of the inner square in inches
Explanation:
The area of a square can be calculated by squaring its side length.
The area of the inner square in the center of the rug is x^2 square inches.
The side length of the outer region of the rug is equal to the sum of the side length of the inner square and twice the width of the outer region. This can be expressed as:
x + 2(11) = x + 22
Therefore, the side length of the outer region of the rug is x + 22 inches.
The area of the outer region of the rug can be calculated by subtracting the area of the inner square from the area of the larger square:
Area of outer region = (x + 22)^2 - x^2
Expanding the expression, we get:
Area of outer region = x^2 + 44x + 484 - x^2
Simplifying, we get:
Area of outer region = 44x + 484 square inches