Question

Find length and breadth of a rectangular park whose perimeter is 100 m and area is 600 m².

Answer 1

Let length of a rectangular park be ‘l’ m and breadth ‘b’ m.

Perimeter = 100 m

2(l + b) = 100

l + b = 50

l = 50 – b   .....(1)

∵ Area = 600 m²

lb = 600

Substitute value of ‘l’ from equation (1)

(50 – b)b = 600

⇒ 50b – b² = 600

⇒ b² – 50b + 600 = 0

⇒ b² – 30b – 20b + 600 = 0

⇒ b(b – 30) – 20(b – 30) = 0

⇒ b = 30 or 20

When b = 30 m

l = 50 – 30

l = 20 m

When b = 20 m

l = 50 – 20

l = 30 m

Hence, the length and breadth of a rectangular park are 20 m and 30 m or 30 m and 20 m, respectively.