Question

find the number of side of a polygon which has 20 diagonals​

Answer 1

Here is your answer:-

You can set n(n-3)/2 = 20, expand and solve the quadratic equation by factorization but this is time consuming and inefficient. Way faster is to simply plug in the answer choices for n and see which one satisfies the equation: n(n-3) = 40. Ans: n=8. 20=(n^2-3n)/2 

40=n^2-3n 

n^2-3n-40= 0 

Splitting the middle term, 

n^2-8n+5n-40=0 

n(n-8)+5(n-8)=0 

(n-8)(n+5)= 0 

So there are two values for n 

n-8=0 or n+5=0 

n = 8 or n = -5 

n can’t be negative 

So n = 8 

Hence the sides are 8 in number.

Hope this helps you ♥️✌

Answer 2

$\huge\fbox\red{A}\fbox\orange{n}\fbox\purple{s}\fbox\green{w}\fbox\pink{e}\fbox\blue{r}$

20=(n^2-3n)/2

40=n^2-3n

n^2-3n-40= 0

Splitting the middle term,

n^2-8n+5n-40=0

n(n-8)+5(n-8)=0

(n-8)(n+5)= 0

So there are two values for n

n-8=0 or n+5=0

n = 8 or n = -5

n can’t be negative

So n = 8