A convex polygon has 44 diagonals. The polygon is

Question

A convex polygon has 44 diagonals. The polygon is (A) nonagon (B) decagon (C) undecagon (D) Dodecagon

Tardigrade Admin · Accepted Answer

If number of sides is n, then total number of diagonals of a convex polygon = n C 2- n =44 (given) ⇒ n ( n -1)-2 n =88 ⇒ n 2-3 n -88=0 ⇒ ( n -11)( n +8)=0 ⇒ n =11 ⇒ undecagon

Q. A convex polygon has 44 diagonals. The polygon is

nonagon

decagon

undecagon

Dodecagon

If number of sides is $n$ , then
total number of diagonals of a convex polygon $=^{n} C_{2} - n = 44$ (given)
$\Rightarrow n (n - 1) - 2 n = 88 \Rightarrow n^{2} - 3 n - 88 = 0 \Rightarrow (n - 11) (n + 8) = 0$
$\Rightarrow n = 11 \Rightarrow$ undecagon

Q. A convex polygon has 44 diagonals. The polygon is

nonagon

decagon

undecagon

Dodecagon

If number of sides is n, then total number of diagonals of a convex polygon =nC2​−n=44 (given) ⇒n(n−1)−2n=88⇒n2−3n−88=0⇒(n−11)(n+8)=0 ⇒n=11⇒ undecagon

If number of sides is $n$ , then
total number of diagonals of a convex polygon $=^{n} C_{2} - n = 44$ (given)
$\Rightarrow n (n - 1) - 2 n = 88 \Rightarrow n^{2} - 3 n - 88 = 0 \Rightarrow (n - 11) (n + 8) = 0$
$\Rightarrow n = 11 \Rightarrow$ undecagon