Arectangular garden has an area of 32 square yards if the length is 4 feet more than the width what is the perimeter of the yard

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

the first option is the answer.