Question

Question 5
Is it possible to design a rectangular park of perimeter 80 and area 400 $m^2$? If so find its length and breadth.

Answer 1

Let the length and breadth of the park be l and b.
Perimeter = 2 (l + b) = 80
l + b= 40
Or,b= 40 -l
$Area=l\times b=l(40-l)=40l-l^2=400$
$\Rightarrow$ $l^2-40l+400=0$
Comparing this equation with $a{x}^2+bx+c=0$, we get
a = 1, b = -40, c = 400
$Discriminant=b^2-4ac$
= $(-40{)}^2-4\times 400$
= 1600 - 1600
= 0
Therefore, this equation has equal real roots. And hence, this situation is possible.
Root of this equation $=\frac{-b}{2a}$ = $\frac{40}{2\times 1}$ = $\frac{40}{2}$ = $20$
Therefore, length of the park,l= 20 m
and breadth of the park, b= 40 -l= 40 - 20 = 20 m.
So the park will be of square shape with a side length of 20m.