Explanation:

Given, Perimeter of rectangle = 82 m and Area of rectangle = 400 m²
Let, length = l   and   breadth = b
∴  Perimeter of rectangle = 82 m
2(l + b) = 82
l + b = 41
l = 41 – b          ...(i)
And, Area of rectangle = 400 m²
l × b = 400
(41 – b) × b = 400        [From eq. (i)]
41b – b² = 400
b² – 41b + 400 = 0
b² – 25b – 16b + 400 = 0
b(b – 25) – 16(b – 25) = 0
(b – 16) (b – 25) = 0
b = 16 m or 25 m
Hence, breadth = 16 m