Question

the equation d=1/2n (n-3) gives the number of diagonals D for polygon with n sides. use this equation to find the number of sides n for a polygon that has 65 diagonals

Answer 1

To solve this problem you must apply the proccedure shown below:

 1. You have that:

 - The equation d=1/2(n(n-3)) gives the number of diagonals for the polygon.

 - The polygon that has 65 diagonals..

 2. When you clear n, you obtain:

 d=n(n-3)/2
 d=(n^2-3n)/2
 2x65=n^2-3n
 n^2-3n-130=0
 
 3. When you solve the quadratic equation, you obtain:

 n=13

 Therefore, the answer is: 13 sides.  

Answer 2

Answer:  13

Step-by-step explanation:

Given : The equation $d=\dfrac{1}{2}n(n-3)$ gives the number of diagonals d for polygon with n sides.

To find the number of sides n for a polygon that has 65 diagonals, we substitute the value of d= 65 in the given equation, we get

$65=\dfrac{1}{2}n(n-3)$

Multiply 2 on both sides , we get

$n(n-3)=130\\\\\Rightarrow\ n^2-3n-130=0\\\\\Rightarrow\ n^2-13n+10n-130=0\\\\\Rightarrow\ n(n-13)+10(n-13)=0\\\\\Rightarrow\ (n-13)(n+10)=0\\\\\Rightarrow\ n= -10\ or\ n= 13$

But number of sides cannot be negative, so the number of sides n for a polygon that has 65 diagonals = 13