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