The length of a rectangle is 5 inches more than its width, x. The area of a rectangle can be represented by the equation x 2 + 5x = 300. What are the measures of the width and the length?

1. Given that the width of the rectangle is x, and the area of the rectangle may be represented by the equation x^2 + 5x = 300, we can solve this equation for the width (x) as such:

x^2 + 5x = 300

x^2 + 5x - 300 = 0 (Subtract 300 from both sides)

(x - 15) (x + 20) = 0 (Factorise x^2 + 5x - 300)

From this, we get: x = 15 or x = - 20

Since the width must be a positive length (ie. more than 0), - 20 would be an invalid answer in the given context and thus the width is given by x = 15.

2. If we know that the length is 5 inches more than the width, we simply need to add 5 to the width we found above to obtain the length:

Length = x + 5

Length = 15 + 5 = 20

Thus, the width of the rectangle is 15 inches and the length of the rectangle is 20 inches.