Question

Naveen made a bangle of silver wire, of diameter 35 mm. It is rebent into a square form. Determine the length of the side of the square.

Answer 1

Hint: In this type of question we have to use the concept of perimeter of different geometrical shapes. Here, we have given the diameter of the bangle so we can find the perimeter of the bangle which is the same as that of the perimeter of square shape made by rebending the bangle. Then by using this perimeter we can find the length of the side of the square. We know that, the perimeter of the circle that is circumference of the circle is given by, \[2\pi r\] where \[r\] is the radius of the circle and the perimeter of the square is given by, \[4\times \left( Side \right)\].

Complete step-by-step solution:
Now we have to determine the length of the side of the square which is formed by rebending the bangle having a diameter 35 mm.
Let us find the perimeter of the bangle.
\[\Rightarrow \text{Perimeter of Circle = }2\pi r\]
As the diameter of the bangle is 35 mm, its radius is \[r=\dfrac{35}{2}mm\].
\[\begin{align}
  & \Rightarrow \text{Perimeter of Circle = }2\times \dfrac{22}{7}\times \dfrac{35}{2} \\
 & \Rightarrow \text{Perimeter of Circle = 22}\times \text{5} \\
 & \Rightarrow \text{Perimeter of Circle = }110mm \\
\end{align}\]
Now, the bangle is rebent to form a square, hence
\[\begin{align}
  & \Rightarrow \text{Perimeter of Square = Perimeter of Circle} \\
 & \Rightarrow \text{Perimeter of Square = }110mm \\
\end{align}\]
But we know that, the perimeter of square is given by the formula, \[4\times \left( Side \right)\]
\[\begin{align}
  & \Rightarrow 4\times \left( Side \right)=110mm \\
 & \Rightarrow Side=\dfrac{110}{4}mm \\
 & \Rightarrow Side=27.5mm \\
\end{align}\]
Hence, the length of the side of the square is \[27.5mm\].

Note: In this type of question students have to note that by rebending any shape we can obtain a new shape at that time the perimeter of the shape remains the same but the area of the shape changes, so that they have to use perimeter and area. Also students have to remember the formulas of perimeter of the different geometrical shapes.