# Is it possible to design a rectangular park of perimeter 80 m

Question:

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

Solution:

Let the breadth of the rectangle be $=x$ metres . Then

Perimeter $=80$ metres

$2($ length $+$ breadth $)=80$

$($ length $+x)=40$

length $=40-x$

And area of the rectangle

length $\times$ breadth $=400$

$(40-x) x=400$

$40 x-x^{2}=400$

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

$x^{2}-20 x-20 x+400=0$

$x(x-20)-20(x-20)=0$

$(x-20)(x-20)=0$

$(x-20)^{2}=0$

$(x-20)=0$

$x=20$

Yes, it is possible.

Hence, breadth of the rectangular park be 20 metres and length be 20 metres