The length of a rectangle is 3 inches more than its width. the area of the rectangle is 40 square inches. what is the length, in inches, of the rectangle?

Since width is the smaller value, set width=x. That wold mean that length=x+3. Since Area=width*length, 40=x (3+x). Distribute the x to give you 40=3x+x^2. Set the equation equal to 0 giving you x^2+3x-40=0. Factor the equation to give you (x+8) (x-5) = 0. Set each factor equal to 0. x+8=0 gives you x=-8 & x=-5 gives you x=5. Since we're working with lengths of objects, it can't be negative. Therefore, your width is 5. To find length, substitute width into the original expression (x+3). Therefore, length is 5+3=8.