Answer:
To find the dimensions of the rectangle, we need to factor the trinomial x^2 - 9x - 22 into two binomials. We can do this by looking for two numbers that multiply to -22 and add up to -9. After some trial and error, we find that -11 and 2 satisfy this condition:
x^2 - 9x - 22 = (x - 11)(x + 2)
Now we know that the area of the rectangle is given by the product of its length and width, which are represented by the two binomials above. Specifically, the length of the rectangle is (x - 11) and the width of the rectangle is (x + 2).
Therefore, the dimensions of the rectangle are (x - 11) by (x + 2).
Note: It's worth noting that if we wanted to find the value of x for which the area of the rectangle is maximized, we would need to take the derivative of the area function and set it equal to zero. However, since the problem only asks for the dimensions of the rectangle, we do not need to find the value of x.