Question

If the length of the rectangle is increased by $230$% , its area becomes $828$ sq.cm and perimeter $162$ cm. What is the perimeter of the original rectangle ( in cm ) ?

Answer 1

Let original area be $100$ sq. cm
If length of square increase by $230\%$ then its area also increases by $230\%$.
Increase in area $=230\%$

So, area become $(100+(230\%$ of $100\left)\right)=330$ sq.cm

Given, new area $=828$ sq.cm
Now on comparing, we get
$330=828$
$\Rightarrow 1=\frac{282}{330}$
$\Rightarrow 100=\frac{(828\times 100)}{330}=251$ sq.cm (approx)
Area of square $=a\times a$
$\Rightarrow a\times a=251$
$\Rightarrow a=15.84$ cm
Original perimeter $=4a=4\times 15.84=64$ cm (approx).