Question

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

Answer 1

Length of the rectangle $=12\frac{1}{2}cm$

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

$$\begin{gathered} =\frac{2\times 12+1}{2} \\ =\frac{24+1}{2} \\ =\frac{25}{2} \end{gathered}$$
The breadth of the rectangle $=10\frac{2}{3}cm$

$$\begin{gathered} =\frac{3\times 10+2}{3} \\ =\frac{30+2}{3} \\ =\frac{32}{3} \end{gathered}$$
The perimeter of a rectangle $=2$ (length $+$ breadth)

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

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

Therefore, the perimeter of a rectangle$=46\frac{1}{3}$