Question

Find the missing length of the given figure.

A) 6 cm
B) 4 cm
C) 2 cm
D) 5 cm

Answer 1

Hint:
Here, we need to find the missing length of the side of the figure. We will obtain the missing length by substituting the other lengths in the formula for perimeter of a figure, and then simplify the equation.
Formula Used: Here, we will be using the formula of perimeter, \[{\rm{Perimeter}} = {\text{Sum of all sides}}\].

Complete step by step solution:
The perimeter of a figure is the sum of all of its sides.
We can find the missing length of the side of the figure using the perimeter and the given lengths of the figure.
Let the missing length be \[x\] cm.
The given figure has four sides. The perimeter of the figure will be the sum of the lengths of all the four sides.
We can write this in the form of an equation.
Substituting the lengths 4 cm, 5 cm, 8 cm, and the perimeter as 23 cm, we get
\[\begin{array}{l}{\rm{Perimeter}} = {\text{Sum of all sides}}\\23 = 4 + 5 + 8 + x\end{array}\]
Now, we will add the terms on the right side of the equation to get
\[23 = 17 + x\]
Next, we will subtract 17 from both sides of the equation to get the value of \[x\].
\[\begin{array}{l}23 - 17 = 17 + x - 17\\6 = x\end{array}\]
Therefore, we get the missing length of the side of the given figure as 6 cm.

Hence, the correct option is option (A).

Note:
We can also solve this question by checking each given option and verifying which options give the perimeter of the figure as 23 cm. For example, to verify option (B), we will check the sum of the lengths 4 cm, 5 cm, 8 cm and 4 cm. The perimeter of the figure will be \[4 + 5 + 8 + 4 = 21\] cm. This is incorrect since the perimeter is given as 23 cm. Hence, we find that the missing length cannot be 4 cm. Similarly, we can check for the other options and find that the missing length is 6 cm.