+0  
 
0
7
2
avatar+1839 

The number of diagonals in a certain regular polygon is equal to $2$ times the number of sides.  How many sides does this polygon have?

 Dec 18, 2023
 #1
avatar+671 
0

In a regular polygon with n sides, we can draw nC2 diagonals (excluding the n sides themselves). Therefore, we have the equation:

 

nC2 = 2n

 

To solve for n, we can rewrite the binomial coefficient using factorials:

 

n(n-1) / 2 = 2n

 

Simplifying the equation:

 

n(n-1) = 4n

 

n^2 - n - 4n = 0

 

n^2 - 5n = 0

 

Factoring the equation:

 

n(n-5) = 0

 

Therefore, the possible values of n are 0 and 5. However, a regular polygon cannot have 0 sides. So, the only valid solution is n = 5.

 

Therefore, the regular polygon has 5 sides. This corresponds to a pentagon, where the number of diagonals (10) is indeed twice the number of sides (5).

 Dec 18, 2023
 #2
avatar+14 
0

I have a knowledge based answer, it is simply 7 because heptagons have 14 diagonals. 

 Dec 18, 2023

5 Online Users

avatar
avatar
avatar