Ex 2.1 Q4 Fractions and decimals Solution- NCERT Maths Class 7

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 A rectangular sheet of paper is \(\begin{align}12\frac{1}{2} \,\rm{cm}\end{align}\) long and \(\begin{align}10\frac{2}{3}\,\rm{cm}\end{align}\) wide. Find its perimeter.

Text Solution

What is Known?

Length and breadth of a rectangular sheet of paper.

What is unknown?

 Perimeter of the sheet.


Perimeter of a rectangle can be calculated easily by adding lengths of four sides of the rectangle.


Length of rectangular sheet  \(\begin{align}=12\frac{1}{2}\,\text{cm}=\frac{25}{2}\,\text{cm}\end{align}\) 

Breadth of rectangular sheet  \(\begin{align}=10\frac{2}{3}\,\text{cm}=\frac{32}{3}\,\text{cm}\end{align}\)

We know that,

\[\begin{align} \text{Perimeter of Rectangle}&=2 (\rm{Length}\,+ \, \rm{Breadth})\\& =2\left( \frac{25}{2}+\frac{32}{3} \right) \\ & =2\left( \frac{25\times 3+32\times 2}{2\times 3} \right) \\ & =2\left( \frac{75+64}{6} \right) \\ & =2\left( \frac{139}{6} \right) \\ & =2\times \left( \frac{139}{6} \right) \\ & =46\frac{1}{3}\text{cm} \end{align}\]

Therefore, perimeter of rectangular sheet of the paper is \(\begin{align}46\frac{1}{3}{\rm{cm}}\end{align}\)

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