maths polygon ques. help please...

Question

ABCD is a convex quadrilateral. 3,4,5 and 6 points are marked on the sides AB, BC,CD and DA

 respectively . The number of the triangles  with vertices on different sides  is ?

•  270
•  220
•  282
• none of these  

Answer 1

I'll assume the question means that all three vertices must be on different sides.

 

 

The three vertices might be on sides AB, BC, and CD; sides AB, BC, and DA; sides AB, CD, and DA; or sides BC, CD, and DA. Let's explore each of the four possibilities.

 

 

AB, BC, CD:

 

We need to choose one of the 3 points on AB, one of the 4 points on BC, and one of the 5 points on CD. That's a total of:

 

3×4×5 = 60 possible choices

 

 

AB, BC, DA:

 

Choose one of the 3 points on AB, one of the 4 points on BC, and one of the 6 points on DA:

 

3×4×6 = 72 possible choices

 

 

AB, CD, DA:

 

3×5×6 = 90 possible choices

 

 

BC, CD, DA:

 

4×5×6 = 120 possible choices

 

 

That's a total of:

 

60+72+90+120 = 342 triangles