Question

Find the missing length in the given figure.

Answer 1

Hint: We should know that the sum of all sides of a polygon is equal to the perimeter of the polygon. Let us assume the length of the side CD is equal to x cm. Let us assume the perimeter of the figure is equal to p. Now we will substitute the given values in p. This will give us the value of x. We know that x will give us the length of CD. We also know that the length of a CD is equal to length of missing length.

Complete step-by-step answer:
Before solving the question, we should know that the sum of all sides of a polygon is equal to the perimeter of the polygon.

From the diagram, it is clear that the length of side AB is equal to 5 cm, length of side BC is equal to 4 cm, length of side AD is equal to 8 cm and perimeter of ABCD is equal to 23 cm.
Let us assume the length of the side CD is equal to x cm. Let us assume the measure of perimeter of ABCD is equal to p.
\[p=AB+BC+CD+DA......(1)\]
We know that the length of side AB is equal to 5 cm, length of side BC is equal to 4 cm, length of side AD is equal to 8 cm and perimeter of ABCD is equal to 23 cm.
So, let us assume
\[\begin{align}
  & AB=5cm.....(2) \\
 & BC=4cm.......(3) \\
 & AD=8cm.......(4) \\
\end{align}\]
Now let us substitute equation (2), equation (3) and equation (4) in equation (1).
\[\begin{align}
  & \Rightarrow p=5+4+8+x \\
 & \Rightarrow p=17+x......(5) \\
\end{align}\]
We know that the perimeter of the given figure is equal to 23 cm.
So, we get
\[\begin{align}
  & \Rightarrow 17+x=23 \\
 & \Rightarrow x=6.....(6) \\
\end{align}\]
So, the missing length is equal to 6 cm.

Note: Students should know the perfect definition of perimeter. If a student did not have a clear view on the concept of perimeter, then it is not possible to do this question. So, a clear view is required to solve this problem. Students should be careful at calculation part of this question. If a small mistake is made, then it is not possible to get a correct final answer. So, one should do the calculation part in a perfect manner.