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:
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:
1
8
10
12
The Correct Option is C
Solution and Explanation
The correct option is: (C) 10.
Number of diagonals=2n(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.
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