Question

is it possible to design a rectangular Park of perimeter 80m and area 400 square if so find its length and breadth ​

Answer 1

Answer
Let the length be l m and the breadth be b m.

Then the area would be lb=400

Perimeter would be 2(l+b)=80

lb=400

⇒2(l+b)=80

⇒l+b=40

∴b=40−l --(1)

Substituting (1) in Area, we get

⇒l(40−l)=400

⇒40l−l
2
=400

⇒l
2
−40l+400=0

⇒(l−20)(l−20)=0

∴l=20

has equal roots, so it is possible to design the rectangle of given parameters.

⇒b=40−20=20

We now know that the length of the park is 20 m and the breadth of the park is also 20 m.