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

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Question

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.

Reasoning:

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.

Steps:

Given,

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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