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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 $20\ m$.