Is it possible to design a rectangular park of perimeter 80 m and… - Vidyadip

Question

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

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Answer

Let the breadth of the rectangle be = xmeters. 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.

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