Question

The sides of a rectangle are 250mm and 1.5m. The perimeter in cm is
$\begin{align}
  & \left( a \right)450 \\
 & \left( b \right)350 \\
 & \left( c \right)250 \\
 & \left( d \right)550 \\
\end{align}$

Answer 1

Hint: To solve the question above, first we will convert the sides given into cms because we have to find the perimeter in cms. Then we will look at the definition of perimeter and rectangle and accordingly we will find the perimeter of the given rectangle.

Complete step by step solution:
In the question, it is given that we have to find the perimeter of a given rectangle. Before doing this, we must know what is a rectangle and what is perimeter. A rectangle is a polygon with four sides and the angle between each adjacent side is ${{90}^{\circ }}$. Also the opposite sides of a rectangle are equal in measurement. The perimeter of any polygon is defined as the sum of length of all its sides. In our question, only two sides of the rectangle are given. The other two sides may be found out using the concept that opposite sides of a rectangle are equal.

From the above figure, we can say that: AB=CD and AD=BC. Thus, CD=1.5m and AD=250mm.
Now, we have determined the lengths of all the sides of the rectangle, we can find its perimeter. But before that, we will convert the sides of this rectangle into cm. For this, we are going to use following conversions:
$\begin{align}
  & 1cm=10mm \\
 & 1m=100cm \\
\end{align}$
Thus, we have:
$\begin{align}
  & AB=CD=1.5m \\
 & \Rightarrow AB=CD=1.5\times 100cm \\
 & \Rightarrow AB=CD=150cm \\
\end{align}$
Similarly, we can also say that:
$\begin{align}
  & AD=BC=250mm \\
 & \Rightarrow AD=BC=25\times 10mm \\
 & \Rightarrow AD=BC=25cm \\
\end{align}$
Now, the perimeter is the sum of lengths of all sides. So the perimeter of rectangle ABCD will be given by: Perimeter=AB+BC+CD+AD
$\begin{align}
  & \Rightarrow Perimeter=150cm+25cm+150cm+25cm \\
 & \Rightarrow Perimeter=350cm \\
\end{align}$
Hence, option (b) is correct.

Note: While solving the question, we have first found the length of all the sides and then we have calculated the perimeter of the given rectangle. Instead of calculating the remaining sides of rectangle, we can directly apply the formula of perimeter of rectangle which is shown below: perimeter=2(L+B)
Where L is the length and B is the breadth. Therefore:
$\begin{align}
  & \Rightarrow Perimeter=2\left( 1.5m+250mm \right) \\
 & \Rightarrow Perimeter=2\left( 150cm+25cm \right) \\
 & \Rightarrow Perimeter=2\left( 175cm \right) \\
 & \Rightarrow Perimeter=350cm. \\
\end{align}$