Ex.11.1 Q4 Perimeter and Area - NCERT Maths Class 7

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The perimeter of a rectangular sheet is \(100 \,\rm{}cm.\) If the length is \(35 \,\rm{}cm,\) find its breadth. Also find the area.

Text Solution


What is known?

The perimeter of a rectangular sheet and the length.

What is unknown?

The area and breadth of rectangular sheet.


Perimeter of the rectangular sheet is \(100 \,\rm{}cm\) and its length is \(35 \,\rm{}cm.\) By using the formula of perimeter of rectangle, find the breadth of rectangular sheet. Once length and breadth of rectangular sheet are known, area of rectangular sheet can be calculated.



Perimeter of a rectangular sheet \(= 100 \,\rm{}cm\)

Length of a rectangular sheet \(= 35 \,\rm{}cm\)

Let, the breadth \(= b \,\rm{}cm\)

\[\begin{align}\text{Perimeter of a rectangular sheet} &= {\rm{2}}\left( {{\rm{Length}} + {\rm{Breadth}}} \right)\\{\rm{100}} &= {\rm{2}}\,l + {\rm{2}}\,b\\{\rm{100}} &= {\rm{2}} \times {\rm{35}} + {\rm{2}}\,b \\{\rm{100}} &= {\rm{70}} + {\rm{2}}\,b\\{\rm{2}}\,b &= {\rm{100}} - {\rm{70}}\\b &= \frac{{{\rm{30}}}}{{\rm{2}}}\\b &= {\rm{15 }}\,\rm{}cm\end{align}\]

\[\begin{align}\text{Area of a rectangular sheet} &= {\rm{Length}} \times {\rm{Breadth}}\\&= 35 \times 15{\rm{ }}\\&= 525{\rm{ }}\,\rm{}c{m^2}\end{align}\]


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