Question 97

P.....Q
R.....S
T.....U
V.....W
Using 5 dots in each of the lines PQ, RS, TU and VW as the vertices, how many triangles can be drawn such that the base is on any one of the above lines?

Solution

The base on any one of the lines can be formed in $$5_{C_2}=10\ ways$$

To form a triangle, the base has to be joined to any of the 15 points on the other lines

Number of triangles that can be drawn when the base is on any of the lines = 10 *15 =150

and number of triangles that can be drawn totally = 150*4 = 600

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