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How many triangles can be formed by joining the vertices of an n-sided polygon? How many these triangles have (i) Exactly one side common with that of the polygon? (ii) Exactly two sides common with that of the polygon? (iii) No side common with that of the polygon? I am able to find out how many triangles can be made using the three vertices. but i am not able to unerstand the next three subquestions


How many triangles can be formed by joining the vertices of an 
n-sided polygon?

How many these triangles have


        (i) Exactly one side common with that of the polygon?


        (ii) Exactly two sides common with that of the polygon?


        (iii) No side common with that of the polygon?


I am able to find out how many triangles can be made using the three vertices. but i am not able to unerstand the next three subquestions


Grade:11

2 Answers

SHANTANU JHA
6 Points
8 years ago
i) one side i.e 2 points of triangle can be selected in n ways. then 3rd point can be selected in (n-4) ways.hence n(n-4)ii) two sides can be chosen in 5C2 waysiii)0
anup kumar
14 Points
8 years ago

(i) when one side iscommon then the no. of triangle will be n(n-3)

(ii) when two sides common with the polygon then it will be n

(iii) When no side is common with the polygon then it will be total - when one side is common - when two side is common

i.e C(n,3) - n(n-3)-n

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