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
Answer: the length = 3 u.
