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

Given:

Perimeter of the rectangular park $=80\ m$.

Area of the park$=400\ m^2$.

To do:

We have to find length and breadth of the park if it is possible to design with the given conditions.

Solution:

Let the breadth of the rectangular park be $x$ m and the length of the rectangular park be $y$ m.

This implies,

$2(x+y)=80$

$x+y=40$

$y=40-x$-----(1)

According to the question,

$x \times y=400$

$x(40-x)=400$   (From equation(1) )

$40x-x^2=400$

$x^2-40x+400=0$

$x^2-2(20)(x)+(20)^2=0$ 

$(x-20)^2=0$

$x-20=0$   (Taking square root on both sides)

$x=20$

Therefore, breadth of the park$=20\ m$.

$y=40-20=20\ m$

The breadth of the park is $20\ m$ and the length of the park is $20\ m$.

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Updated on: 10-Oct-2022

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