The length of a rectangle is 4 units less than the width. the area of the rectangle is 21 units. what is the length, in units, of the rectangle?

The formula of an area of a rectangle:

A = wl

We have l = w - 4 and A = 21.

Substitute:

w(w - 4) = 21       use distributive property

(w)(w) + (w)(-4) = 21

w² - 4w = 21     subtract 21 from both sides

w² - 4w - 21 = 0

w² - 7w + 3w - 21 = 0

w(w - 7) + 3(w - 7) = 0

(w - 7)(w + 3) = 0 ↔ w - 7 = 0 ∨ w + 3 = 0

w = 7 ∨ w = -3 < 0

l = w - 4 → l = 7 - 4 = 3