Question

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

Answer 1

Let the length be $l$ m and the breadth be $b$ m.

Then the area would be $lb=400$

Perimeter would be $2(l+b)=80$

$lb=400$

$\Rightarrow 2(l+b)=80$

$\Rightarrow l+b=40$

$\therefore b=40-l$ --(1)

Substituting (1) in Area, we get

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

$\Rightarrow 40l-l^2=400$

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

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

$\therefore l=20$

has equal roots, so it is possible to design the rectangle of given parameters.

$\Rightarrow b=40-20=20$

We now know that the length of the park is $20$ m and the breadth of the park is also $20$ m.