Question

In a triangle ABC, there are 3, 4 and 5 points on side AB, BC, CA respectively. How many triangles will be formed by these points?

Answer 1

Total number of points on side AB, BC and CA = 3 + 4 + 5 = 12 

Hence, number of triangles formed by 12 points

Now, there are 3 points on side AB.

Hence, number of triangle formed by these points

These are 4 points on side BC.

Hence, number of triangles formed by these points

There are 5 points on side CA.

Hence, number of triangle formed by these points

Points on sides AB, BC and CA are collinear.

Hence, any triangle cannot be formed by these points 

Hence, total number of required triangles = 220 – 1 – 4 – 10 = 205.