Polygon diagonals

**yorkey** · May 2nd 2011, 03:53 AM

Please don't shoot if this is in the wrong section. I'm pretty sure its not, but I've said that before. I think it should go in this section because its actually an algebraic sum.. right?

Anyway. I've got this problem:
A polygon with $n$ sides has a total of $\frac{1}{p}$ $n(n-q)$ diagonals, where $p$ and $q$ are integers.

Find the values of $p$ and $q$ .

I don't know what to do! There are no integers in the sum to start with...

**Plato** · May 2nd 2011, 04:18 AM

Originally Posted by yorkey

this problem:
A polygon with $n$ sides has a total of $\frac{1}{p}$ $n(n-q)$ diagonals, where $p$ and $q$ are integers.
Find the values of $p$ and $q$ .

A polygon with n sides has $\binom{n}{2}-n$ diagonals.

**yorkey** · May 2nd 2011, 04:35 AM

Are you saying they gave the wrong formula?

**Plato** · May 2nd 2011, 04:48 AM

Originally Posted by yorkey

Are you saying they gave the wrong formula?

No indeed!
I am saying you can use what I wrote to solve the problem.

**earboth** · May 2nd 2011, 04:50 AM

Originally Posted by yorkey

Please don't shoot if this is in the wrong section. I'm pretty sure its not, but I've said that before. I think it should go in this section because its actually an algebraic sum.. right?

Anyway. I've got this problem:
A polygon with $n$ sides has a total of $\frac{1}{p}$ $n(n-q)$ diagonals, where $p$ and $q$ are integers.

Find the values of $p$ and $q$ .

I don't know what to do! There are no integers in the sum to start with...

1. Examine a number of polygons:

3gon ---> 0 diagonals
4gon ---> 2 diagonals
5gon ---> 5 diagonals

2. Use the given equation, sub in the values you've found in #1 and solve for p, q:

$\left|\begin{array}{r}\frac1p \cdot 4(4-q)=2 \\\frac1p \cdot 5(5-q)=5 \end{array}\right.$

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