Correct Answer - Option 1 : 11
Concept:
- If the number of sides of this polygon is n, therefore the number of vertices will also be n.
- If we draw a line by joining any of these n points, the lines will either be diagonal or a side of the polygon.
- Hence, the total number of lines that can be drawn using these points is equal to the total number of ways of selecting two points out of n points.
- A total number of lines formed using n vertices = Number of diagonal + Number of sides.
Formula used:
The total number of ways of selecting r objects out of n objects nCr
Where, \(^nC_r\ =\ \frac{n!}{r!(n\ -\ r)!}\)
Number of diagonal which can be drawn from n side polygon = nCr - n
Calculation:
Given that,
Number of diagonal = 44
Let, number of sides is n
We know that,
Number of diagonal from n side = nCr - n
\(⇒\ 44 = {^nC_2}-n = \frac{n!}{r!(n\ -\ r)!}\)
\(⇒\ 44 = \frac{1}{2}n(n-1)-n\)
⇒ n2 - 3n - 88 = 0
⇒ n2 - 11n + 8n - 88 = 0
⇒ n(n - 11) + 8(n - 11) = 0
⇒ n = 11 and n = - 8
since n ≠ - 8
Hence, total number of side is 11.