Ex.11.1 Q6 Perimeter and Area - NCERT Maths Class 7

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Question

A wire is in the shape of a rectangle. Its length is \(40 \,\rm{} cm\) and breadth is \(22 \,\rm{}cm.\) If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area ?

Text Solution

 

What is known?

A wire is in the shape of a rectangle. Its length is \(40 \,\rm{} cm\) and breadth is \(22 \,\rm{}cm\) and the same wire is rebent in the shape of a square.

What is unknown?

The measure of each side of square and which shape (rectangle or square) encloses more area.

Reasoning:

The wire is initially in the shape of rectangle and the same wire is rebent in the shape of square. This means the perimeter of both the rectangle and square is the same. By using the equations related to perimeter of square and rectangle, we can find the side of the square. Once side of the square is known, its area can be calculated. Similarly, by using the length and breadth of the rectangle, its area can be obtained. Now, by knowing the area of both the shapes you can easily decide which shape encloses more area.

Steps:

Given,

Length of rectangle \(= 40 \,\rm{}cm\)

Breadth \(= 22 \,\rm{}cm\)

Since same length of wire is used to from rectangle and square,

\[\begin{align}{\text{Perimeter of square}} &= {\text{perimeter of rectangle}}\\4 \times {\rm{Side}} &= 2\left( {{\rm{Length}} + {\rm{Breadth}}} \right)\\4 \times {\rm{Side}} &= 2\left( {40 + 22} \right){\rm{ }}\\4 \times {\rm{Side}} &= 2 \times 62{\rm{ }}\\4 \times {\rm{Side}} &= 124\\{\rm{Side}} &= \frac{{124}}{4}\\{\rm{Side}} &= 31\;{\rm{cm}}\end{align}\]

\[\begin{align}\text{Area of square}& = {\rm{side}} \times {\rm{side}}\\& = 31 \times 31\\ &= 961\;{\rm c{m^2}}\end{align}\]

\[\begin{align}\text{Area of rectangle}&= {\rm{Length}} \times {\rm{Breadth}}\\& = 40 \times 22\\&= 880{\rm{ }}{\rm\, c{m^2}}\end{align}\]

Therefore, it is clear from the above that the figure square encloses more area than rectangle.

  
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