The formula of an area of a recangle:
A = lw
We have A = 32 yd² and l = w + 4.
Substitute:
(w + 4)w = 32 use distributive property
(w)(w) + (4)(w) = 32
w² + 4w = 32 subtract 32 from both sides
w² + 4w - 32 = 0
w² + 8w - 4w - 32 = 0
w(w + 8) - 4(w + 8) = 0
(w + 8)(w - 4) = 0 ↔ w + 8 = 0 ∨ w - 4 = 0
w = -8 < 0 ∨ w = 4
l = w + 4 → l = 4 + 4 = 8
w = 4 yd and l = 8 yd.
The formula of a perimeter of a rectangle:
P = 2(l + w)
Substitute:
P = 2(8 + 4) = 2(12) = 24
