The length of a rectangle is 7 meters more than four times its width. If the area of the rectangle is 650 square meters, find its length and width.

Question

The length of a rectangle is 7 meters more than four times its width. If the area of the rectangle is 650 square meters, find its length and width.

Answer 1

If w is the width, then the length is 4w + 7. Area is length times width, so we have the equation:

w(4w + 7) = 650; 4w^2 + 7w = 650; 4w^2 + 7w - 650 = 0. Solve this using the solution to quadratic equation:

w = (-7 + SQRT{49 - [(4)(4)(-650)]}) / (2)(4). I got 11.9 meters for the width, so the length is 11.9(4) + 7 = 54.6 meters. This will indeed give an area of 650 square meters.