If a convex polygon has 35 diagonals, then the number of triangles formed by joining the vertices of the polygon is :
A
84
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
93
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
105
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
120
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is D120 If polygon has n sides, then number of
diagonals is nC2−n=35 ⇒n(n−1)2−n=35
Solving we get n=10.
Thus, there are 10 vertices (as number of sides and vertices in a polygon are always equal) ∴The number of traingles that can be formed =10C3=120.