Final answer:
The width of the rectangle with an area of 121-x^2 square meters and a length of 11 - x meters is represented by the expression 11 + x meters.
Step-by-step explanation:
The area of a rectangle is the product of its length and width. In this case, the area is given as 121-x^2 square meters, while the length is given as 11 - x meters. To find the expression for the width, we divide the area by the length. Therefore, the width w can be represented by the following equation:
w = \(\frac{Area}{Length}\) = \(\frac{121-x^2}{11-x}\).
Due to the structure of the quadratic area (a perfect square difference) and the linear length (a factor of the quadratic), the equation simplifies to:
w = \(\frac{(11+x)(11-x)}{11-x}\).
Canceling out the common factor (11-x), we are left with:
w = 11 + x.
Thus, the expression representing the width of the rectangle is 11 + x meters.