Question: The sides AB, BC, CA, of a triangle ABC have 3, 4 and 5 interior points respectively on them. The total number of triangles that can be constructed by using these points as vertices is
Options:
A) 220
B) 204
C) 205
D) 195
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] We have in all 12 points. Since, 3 points are used to form a triangle, therefore the total number of triangles including the triangles formed by collinear points on AB, BC and CA is $ ^{12}C_3=220. $ But this includes the following: The number of triangles formed by 3 points on $ AB={{}^{3}}C_3=1 $ The number of triangles formed by 4 points on $ BC{{=}^{4}}C_3=4. $ The number of triangles formed by 5 points on $ CA{{=}^{5}}C_3=10. $ Hence, required number of triangles $ =220-(10+4+1)=205. $
BETA
