A rectangular rug is 3 feet longer than it is wide if the area of the rug is 40 square feet find the length and the width?
The area of a rectangle is the product of its length and width. From the statement of the problem, this is w(w + 3) = 40, where w represents the width. Rearranging this equation gives w2 + 3w - 40 = 0. The left side can be factored into (w + 8)(w - 5), which will be zero when w = -8 or 5. A negative number is impossible for a real rug. Therefore the width is 5 feet and the length 5 + 3 = 8 feet.