The sides AB, BC, CA of triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices

Question

The sides AB, BC, CA of triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices (A)  201  (B)  120  (C)  205  (D)  435

Tardigrade Admin · Accepted Answer

Required number of triangles, =12C3-3C3-4C3-5C3 =220-1-4-10 =205

Q. The sides $A B, BC, C A$ of triangle $A BC$ have $3, 4$ and $5$ interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices

$201$

$120$

$205$

$435$

Required number of triangles,
$=^{12} C_{3} -^{3} C_{3} -^{4} C_{3} -^{5} C_{3}$
$= 220 - 1 - 4 - 10$ $= 205$

Q. The sides AB,BC,CA of triangle ABC have 3,4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices

201

120

205

435