The number of diagonals in a polygon is 20. The number of sides of the polygon is

Question

The number of diagonals in a polygon is 20. The number of sides of the polygon is (A) 5 (B) 6 (C) 8 (D) 10

Tardigrade Admin · Accepted Answer

Let n be a side of polygon. Then, number of diagonals of the polygon = n C2-n ⇒ 20=(n(n-1)/2)-n ⇒ n2-3 n-40=0 ⇒ (n+5)(n-8)=0 ⇒ n=8 (∵ n cannot be negative)

Q. The number of diagonals in a polygon is $20$ . The number of sides of the polygon is

5

6

8

10

Let $n$ be a side of polygon.
Then, number of diagonals of the polygon
$=^{n} C_{2} - n$
$\Rightarrow 20 = \frac{n ( n - 1 )}{2} - n$
$\Rightarrow n^{2} - 3 n - 40 = 0$
$\Rightarrow (n + 5) (n - 8) = 0$
$\Rightarrow n = 8 (∵ n$ cannot be negative)

Q. The number of diagonals in a polygon is 20. The number of sides of the polygon is

5

6

8

10

Let n be a side of polygon. Then, number of diagonals of the polygon =nC2​−n ⇒20=2n(n−1)​−n ⇒n2−3n−40=0 ⇒(n+5)(n−8)=0 ⇒n=8(∵n cannot be negative)

Q. The number of diagonals in a polygon is $20$ . The number of sides of the polygon is

Let $n$ be a side of polygon.
Then, number of diagonals of the polygon
$=^{n} C_{2} - n$
$\Rightarrow 20 = \frac{n ( n - 1 )}{2} - n$
$\Rightarrow n^{2} - 3 n - 40 = 0$
$\Rightarrow (n + 5) (n - 8) = 0$
$\Rightarrow n = 8 (∵ n$ cannot be negative)