Question

Is it possible to design a rectangular park of perimeter 80 m and area 400 m-? If so, find
its length and breadth.​

Answer 1

Answer

Yes . Possible . But it's not rectangular but square .

Length , l = 20 m

Breadth , b = 20 m

Given :

• A rectangular park having perimeter 80 m and area 400 m²

To Find :

• Length and breadth

Solution :

Perimeter of rectangle = 2 ( l + b )

⇒ 2 ( l + b ) = 80

⇒ l + b = 40

⇒ b = 40 - l ... (1)

Area of rectangle = lb

⇒ lb = 400

⇒ l ( 40 - l ) = 400 [ From (1) ]

⇒ 40 l - l² = 400

⇒ l² - 40l + 400 = 0

⇒ l² - 20l - 20l + 400 = 0

⇒ l ( l - 20 ) - 20 ( l - 20 ) = 0

⇒ ( l - 20 ) ( l - 20 ) = 0

⇒ l = 20 m

Sub. l value in (1) , we get ,

⇒ b = 40 - 20

⇒ b = 20 m