Question

Area of rectangular playground is $420$ sq.m. If the length of a playground is increased by $7$ meter and breadth is decreased of by $5$ meter; area remain unchanged then find the length and the breadth.

Answer 1

Let the length and breadth of the rectangle be ${}^{\prime }{a}^{\prime }{,}^{\prime }{b}^{\prime }$.

Given area = $420$ sq.m

$\Rightarrow ab=420$ ...(1)

length $\to$ increased by $7$ meter

breadth $\to$ decreased by $5$ meter

Area $\to$ remains unchanged

$\Rightarrow (a+7)(b-5)=420$ ...(2)

From, (1) , $b=\frac{420}{a}$

$\Rightarrow (a+7)(\frac{420}{a}-5)=420$

$\Rightarrow 420-5a+\frac{2940}{a}-35=420$

$\Rightarrow -a^2+588-7a=0$

$\Rightarrow a^2+7a-588=0$

$\Rightarrow a^2+28a-21a-588=0$

$\Rightarrow a(a+28)-21(a+28)=0$

$\Rightarrow a=21m$

$ab=420\Rightarrow b=20m$

$\therefore$ Length $=21m$ and breadth $=20m$