A rectangle has a length of 15
inches less than 5
times its width. If the area of the rectangle is 540
square inches, find the length of the rectangle.
Let's assume the width of the rectangle is x inches.
According to the given condition, the length of the rectangle is 5 times its width minus 15 inches.
Length = 5x - 15 inches.
We know that the area of a rectangle is given by length * width.
So, the area of the rectangle is (5x - 15) * x = 540 square inches.
Expanding the equation, we get 5x^2 - 15x = 540.
Rearranging the equation, we get 5x^2 - 15x - 540 = 0.
Dividing the equation by 5, we get x^2 - 3x - 108 = 0.
By factoring the equation, we get (x - 12)(x + 9) = 0.
So, x - 12 = 0 or x + 9 = 0.
If x - 12 = 0, x = 12 inches.
If x + 9 = 0, x = -9 inches (since width cannot be negative).
Therefore, the width of the rectangle is 12 inches.
Substituting the value of x in the equation for length, we get Length = 5*12 - 15 = 60 - 15 = 45 inches.
Hence, the length of the rectangle is 45 inches. Answer: \boxed{45}.