Question

Please help IN TRIANGLE ABC WITH SIDE AB, BC, CA, _____​

Answer 1

Answer:

First note in all 3 + 4 + 5, that is, 12 points are used for forming the triangles. Since 3 points are needed to form a triangle, the total number of triangles (including the triangle formed by collinear points and as these collinear points will not form . triangles their number has to be subtracted from total) is 12C3=220. But this includes the number of triangles formed by 3 points on AB = 3C3 = 1, the number of triangles formed by 4 points on BC = 4C3 = 4, and the number of triangles formed by 5 points on CA = 5C3 = 10.

Hence the required number of triangles

 = 220-(1 + 4+10) =205.