Q. 54.0( 17 Votes )

# Is it possible to design a rectangular park of perimeter 80m. and area 400m^{2}? If so, find its length and breadth.

Answer :

Let Length of rectangular park be x and breadth be (40 - x)

Area = 400 m^{2}

⇒ x(40 - x) = 400

⇒ x^{2} - 40x + 400 = 0

Discriminant = ( - 40)^{2} - 4 × 1 × 400

⇒ Discriminant = 1600 - 1600 = 0

Since Discriminant is 0 so it is possible

x^{2} - 40x + 400 = 0

⇒ (x - 20)^{2} = 0

⇒ x = 20 m

Answer: Length = 20m, Breadth = 20m

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