# 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.

Video Solution
Perimeter And Area
Ex 11.1 | Question 4

## 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 $$= b \,\rm{}cm$$

Perimeter of a rectangular sheet

\begin{align} &= {\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}

Area of a rectangular sheet

\begin{align} &= {\rm{Length}} \times {\rm{Breadth}}\\&= 35 \times 15{\rm{ }}\\&= 525{\rm{ }}\,\rm{}c{m^2}\end{align}

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