Answer:
length = 8 m
Explanation:
note the area of a room cannot be 32 cm²
so you must mean area = 32 m²
let the width be w then length is w + 4
area (A) of a rectangular room is calculated as
A = length × width
given A = 32 , then
w(w + 4) = 32
w² + 4w = 32 ( subtract 32 from both sides )
w² + 4w - 32 = 0 ← in standard form
(w + 8)(w - 4) = 0 ← in factored form
equate each factor to zero and solve for w
w + 8 = 0 ⇒ w = - 8
w - 4 = 0 ⇒ w = 4
but w must be greater than zero, so w = 4
length = w + 4 = 4 + 4 = 8 m