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polygon

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by moadhia » Thu Feb 26, 2009 8:15 am
In a Polygon,all but one vertices are connected to each other by straight lines and 78 diagonals are formed.How many sides does the polygon have ?


A. 15
B.17
C.12
D.16
E.18

I dont have an OA for this.
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is this correct question

by satish.nagdev » Thu Feb 26, 2009 9:05 am
I don't think this question itself is correct

number of diagonals in n sided polygon = n*(n-3)/2

none of answer choices bring 78

could you please reconfirm?

thanks
satish.
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Re: polygon

by x2suresh » Thu Feb 26, 2009 9:34 am
moadhia wrote:In a Polygon,all but one vertices are connected to each other by straight lines and 78 diagonals are formed.How many sides does the polygon have ?


A. 15
B.17
C.12
D.16
E.18

I dont have an OA for this.



Let n+1 points in the polygon

One vertex is not connected to ..any of the other vertex

so.. Its like polygon with N sides and the link is broken.


Forumula for No.Of diagnols = NC2(select any two points out of N) -N (substracting sides )

Here No.Of diagonals=NC2 -(N-1) ( here one of them is actually not side it is diagnol .. )



N (N-3)/2 = 78 -1 = 77 = 11*14/2

N = 14

N+1 = 15

A is the Answer.
Last edited by x2suresh on Thu Feb 26, 2009 10:27 am, edited 1 time in total.
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by satish.nagdev » Thu Feb 26, 2009 10:19 am
awesome Suresh :)

I din't paid attention properly to all but one thing

thanks for clarifying

cheers,
satish
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