Question

A rectangular playground is 420 sq.m. If its length is increased by 7 m and breadth is decreased by 5 metres, the area remains the same. Find the length of playground.

Answer 1

Let the length of the playground be $l$ and breadth be $b$
Thus, $lb=420$

$\therefore l=\frac{420}{b}$......(1)
Length is increased by $7m$ and breadth is decreased by $5m$

$\therefore (l+7)(b-5)=420$
$(\frac{420}{b}+7)(b-5)=420$.........From (1)
$(420+7b)(b-5)=420b$
$420b+7b^2-35b-2100=420b$
$7b^2-35b-2100=0$
$b^2-5b-300=0$
$b^2-20b+15b-300=0$
$(b-20)(b+15)=0$
$b=20,-15$

Taking only positive value of $b$
Thus, $l=\frac{420}{20}=21m$
Hence, length $=21m$ and breath $=20m$