Question

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

Answer 1

Perimeter of a rectangle$=2(l+b)=80m$

$\Rightarrow l+b=\frac{80}{2}=40m$

$\Rightarrow l=40-b$

And $lb=400m^2$

$\Rightarrow (40-b)b=400$

$\Rightarrow 40b-b^2-400=0$

$\Rightarrow b^2-40b+400=0$

$\Rightarrow b^2-20b-20b+400=0$

$\Rightarrow b(b-20)-20(b-20)=0$

$\Rightarrow (b-20)(b-20)=0$

$\therefore b=20m$

When $b=20m\Rightarrow l=40-b=40-20=20m$

$\therefore$ To design a park length as $20m$ and breadth as $40m$ required.

$\therefore l=40m$ and $b=20m$