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Manager  Joined: 13 Aug 2010
Posts: 142
How many sides does a polygon have, if it has 44 diagonals?  [#permalink]

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How many sides does a polygon have, if it has 44 diagonals?

A polygon has 44 diagonals, and then numbers of sides are?
Retired Moderator Joined: 02 Sep 2010
Posts: 759
Location: London
Re: How many sides does a polygon have, if it has 44 diagonals?  [#permalink]

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prab wrote:
How many sides does a polygon have, if it has 44 diagonals?

A polygon of n sides has n(n-3)/2 diagnols

n(n-3)/2=44 OR n(n-3)=88 OR n=11

Answer is 11
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Manager  Joined: 08 Sep 2010
Posts: 165
Location: India
WE 1: 6 Year, Telecom(GSM)
Re: How many sides does a polygon have, if it has 44 diagonals?  [#permalink]

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Answer is 11.

nC2-n=44

(Combination of two points out of n points)-(number of sides that is equal to number of pints i.e n) = Number of diagonals.

{n(n-1)}/2 - n = 44

solving n=11

Consider Kudos If you like the solution.
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Joined: 11 Jul 2017
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Re: How many sides does a polygon have, if it has 44 diagonals?  [#permalink]

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There is a rule for this:
For any geometric figure, the number of sides is equal to the number of vertexes. Let "n" be that number.

At first, you may think that n.n is the number of diagonals but that is not the case for two reasons.

First, with such procedure, you are counting each line joining two vertexes, including the edges of the figure, which are not diagonals. So, for each vertex, you need to discard two lateral lines. That is n-2. In addition, you need to discard the same vertex you are focusing on. That is n-2-1.

So far, we have n vertexes, each with n-1-2 diagonals coming from it, but that is not the end for a second reason. With n(n-2-1) you are counting each diagonal twice; so divide the number by 2.

The formula is then: n(n-3)/2.

For this question, we have that n(n-3)/2=44. Let's operate.

n(n-3)=88, you can solve the quadratic equation n^2-3n-88 and find that n is equal to 11 (remember that no negative number applies here); or you can notice that 88 must be the result of multiplying 8 x 11. So 11 is the answer.
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Re: A polygon has 44 diagonals, and then numbers of sides are  [#permalink]

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_________________ Re: A polygon has 44 diagonals, and then numbers of sides are   [#permalink] 26 Nov 2018, 02:16
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