Question

The length of a rectangle is $5cm$ less than twice its breadth. If the length is decreased by $5cm$ and breadth is increased by $2cm$, the perimeter of the resulting rectangle will be $74cm$. Find the length and breadth of the original rectangle.

Answer 1

Let the breadth of a rectangle be $x$ cm.

Therefore, the length will be $2x-5$ cm.

Now, length is decreased by $5$ cm i.e., $2x-5-5=2x-10$ cm

and breadth is increased by $2$ cm, i.e., $x+2$ cm.

Also given, perimeter $=74$ cm.

$\Rightarrow 2[2x-10+x+2]=74$

$\Rightarrow$ $2[3x-8]=74$

$\Rightarrow$ $6x-16=74$

$\Rightarrow$ $6x=74+16$

$\Rightarrow$ $6x=90$

$\Rightarrow$ $x=15$

Now, length will be $=2x-5$

$=2\left(15\right)-5$

$=30-5$

$=25$ cm.

Therefore, the length and breadth of a rectangle are $25$ cm and $15$ cm respectively.