Question

The perimeter of the given figure is

\[\begin{array}{*{35}{l}}
   \left( \text{a} \right)\text{ 25 cm} \\
   \left( \text{b} \right)\text{ 21 dm} \\
   \left( \text{c} \right)\text{ 2 m 5 dm} \\
   \left( \text{d} \right)\text{ 2 m 50 dm} \\
\end{array}\]

Answer 1

Hint: In this, we have to find the perimeter of the figure. The perimeter of the figure is the length of the outline of a figure (any shape) or the perimeter of any figure is the sum of all boundaries of a figure.

Complete step-by-step solution:
Before finding the perimeter of the given figure we will consider any simple figure. For example, a rectangle ABCD given as follows.
 

In rectangle ABCD, length of side AB = length of side CD =$x$.
length of side BC = length of side DA =$y$.
Perimeter of a rectangle ABCD = length of side AB + length of side BC+ length of side CD
                                                       + length of side DA.
$\Rightarrow $ Perimeter of a rectangle ABCD = $x+y+x+y.$
$\Rightarrow $ Perimeter of a rectangle ABCD = $2x+2y$.
The given figure is

In the given figure, length of side PQ = 6 dm,
length of side QR = 10 dm,
length of side RS = 4 dm,
length of side PS = 5 dm.
By definition of the perimeter of the figure, we will calculate the perimeter of the given figure as follows,
The perimeter of the given figure PQRS = sum of the length of sides of figure PQRS.
$\Rightarrow $Perimeter of given figure = length of side PQ + length of side QR + length of side RS
                                            + length of side PS
 $\Rightarrow $$\text{Perimeter of given figure =}\left( 6+10+40+5 \right)\text{dm}=25\text{dm}$
Since, 1dm = 0.1m
By using conversion from decimetre to meter, we get
Perimeter of the figure = 2 m 5 dm.
Hence the perimeter of the figure is 2 m 5 dm.
The correct option is (C) .

Note: In this problem, we one should know the conversion of decimetre into the meter and decimetre into centimeter which is 1 dm = 0.1 m and 1dm = 10 cm respectively.
Here we need to keep in mind the basic formula of the perimeter of regular shapes is the sum of all outlines(sides).