# A rectangular sheet of paper is $12\frac{1}{2}\ cm$ long and $10\frac{2}{3}\ cm$ wide. Find its perimeter.

Given :

Length of the rectangular sheet of paper$= 12 \frac{1}{2}\ cm$.

Breadth of the rectangular sheet of paper $= 10 \frac{2}{3}\ cm$.

To do :

We have to find the perimeter of the rectangle.

Solution :

Length $(l)= 12 \frac{1}{2}\ cm$

$= \frac{(12\times 2+1)}{2}\ cm$

$= \frac{(24+1)}{2}\ cm$

$=\frac{25}{2}\ cm$

Breadth $(b)= 10 \frac{2}{3}\ cm$

$= \frac{(10\times3+2)}{3}\ cm$

$= \frac{(30+2)}{3}\ cm$

$= \frac{32}{3}\ cm$

The perimeter of a rectangle of length $l$ and breadth $b$ is $2(l+b)$.

Therefore,

Perimeter of the rectangular sheet of paper $= 2 (\frac{25}{2} + \frac{32}{3})\ cm$

$= 2( \frac{25 \times 3}{2 \times 3} + \frac{32 \times 2}{3 \times 2})$              (LCM of $2$ and $3$ is $6$)

$=2(\frac{75}{6} + \frac{64}{6})$

$= 2(\frac{75+64}{6})$

$= 2(\frac{139}{6})$

$= \frac{139}{3}$

$= 46\frac{1}{3}\ cm$

Therefore, the perimeter of the rectangular sheet of paper is $46\frac{1}{3}\ cm$ .