Question

A table-top measures 2m 25cm by 1m 50cm. What is the perimeter of the table-top?

Answer 1

Hint:To solve this question, first of all, we will find the shape of the table-top. As we know the perimeter of any object is the sum of lengths of its borders. So, after finding the shape of the table-top we can find it’s perimeter by taking the sum of all the lengths of its borders. To find the perimeter we need to have the lengths in a one-unit form which makes the calculation easy. So, firstly we will convert the lengths in mixed units into one-unit form.
The length conversions which we are going to use in solving this question are,
\[\begin{align}
  & 1m=100cm \\
 & 1cm=\dfrac{1}{100}m \\
\end{align}\]

Complete step by step answer:
Till now we have studied many varieties of shapes and their properties. After reading the above question we can see that the opposite sides of the table-top are equal, and all the four sides are not equal to each other. Also, the table-top will have all the angles equal to the right angle.
The shape we studied with these properties is rectangular.

Hence, the shape of the table-top is rectangular.
As we know that the perimeter of rectangle \[=2(length+breath)\]
According to the question, the length is given in mixed units. First of all, we will convert the units into a single units. So, the converted units are as follows,
Length \[=2m\text{ }25cm=2m+\dfrac{25}{100}m=2m+0.25m=2.25m\]
Breath \[=1m\text{ }50cm=1m+\dfrac{50}{100}m=1m+0.50m=1.50m\]
Hence, we will get the perimeter of the table-top as shown below,
\[\begin{align}
  & =2(length+breath) \\
 & =2(2.25+1.50) \\
 & =2\times 3.75 \\
 & =7.50m \\
\end{align}\]
Therefore, the perimeter of the rectangular table-top will be equal to 7.50m of 7m 50cm.
Note:
The error in this question may be in finding the correct shape of the table-top as the wrong shape may or may not give the different value of perimeter. One must also be careful in converting the numerical value of lengths from one unit to another. In the above method, we used the conversion from integral form to decimal form.