Final answer:
To find the length of the rectangle, we need to set up and solve an equation based on its relationship to the width and area.
Step-by-step explanation:
To find the length of the rectangle, we can use the given information about its relationship to the width and area.
Let's assume the width of the rectangle is w inches. According to the problem, the length is 27 inches less than 5 times the width, so the length is 5w - 27 inches.
The formula for the area of a rectangle is length times width, so we have the equation (5w - 27)w = 3690.
Simplifying the equation, we get 5w^2 - 27w - 3690 = 0.
We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. After finding the roots of the equation, we can determine the value of w and then calculate the length by substituting it into the expression 5w - 27.