Question
Mathematics Question on Three Dimensional Geometry
The number of diagonals of a polygon is 35. If A, B are two distinct vertices of this polygon, then the number of all those triangles formed by joining three vertices of the polygon having AB as one of its sides is:
A
1
B
8
C
10
D
12
Answer
10
Explanation
Solution
The correct option is: (C) 10.
Number of diagonals=2 n(n −3)
Given that the number of diagonals is 35, we can set up an equation and solve for n :
n(n −3)=70
Now, we need to find two integers n and n −3 whose product is 70. The pairs of integers that satisfy this condition are (n ,n −3)=(10,7) and (−3)=(35,32)(n ,n −3)=(35,32).
However, in the context of a polygon, the number of sides cannot be negative or zero, so we discard the solution(n ,n −3)=(35,32).
Therefore, the number of sides of the polygon is n =10.