Let the lenght of the park = x
Perimeter = 80 m
Therefore, the breadth = 40 – x m [As Perimeter = 2 (Lenght + Breadth]
According to question,
Area = x (40 – x) = 400
⇒ 40x – x² = 400
⇒ x² – 40x + 400 = 0
⇒ x² – 20x – 20x + 400 = 0
⇒ x(x – 20) – 20(x – 20) = 0
⇒ (x – 20) (x – 20) = 0
⇒ (x – 12)² = 0 or (x – 13) = 0
⇒ (x – 20) = 0
⇒ x = 20
Hence the lenght = 20 m and breadth of the park = 40 – 20 = 20 m.