Question

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

Answer 1

From the given details, we get to know that

Length $=$$12\frac{1}{2}$$cm$

Step:$1$

Here we have a mixed fraction convert into an improper fraction.

Length $=\frac{2\times 12+1}{2}$

$$\begin{gathered} =\frac{24+1}{2} \\ =\frac{25}{2} \end{gathered}$$

Breadth $=$$10\frac{2}{3}$

$$\begin{gathered} =\frac{3\times 10+2}{3} \\ =\frac{30+2}{3} \\ =\frac{32}{3} \end{gathered}$$

Step:$2$

We know that,

The perimeter of the rectangle $=2\times$ (length $+$ breadth)

$$\begin{gathered} =2\times \left(\frac{25}{2}+\frac{32}{3}\right) \\ =2\times \left(\frac{25\times 3}{2\times 3}+\frac{32\times 2}{3\times 2}\right) \\ =2\times \left(\frac{75}{6}+\frac{64}{6}\right) \\ =2\times \left(\frac{75+64}{6}\right) \\ =2\times \frac{139}{6} \\ =\frac{139}{3} \end{gathered}$$

On converting 139/3 into a mixed fraction we get

$\frac{139}{3}=46\frac{1}{3}$

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