Algebra> A polygon has 44 diagonals. The number of...

A polygon has 44 diagonals. The number of its sides is

Samir Madan , 10 Years ago

Grade 12

2 Answers

bharat bajaj

Last Activity: 10 Years ago

Let the polygon has nsides.Then it will have n vertices.
Byjoiningany two vertices, we will get a side or a diagonal.
No. of line segments obtained byjoiningn vertices = NC₂
Out of these n line segments aresidesof the polygon.
So, no. of diagonals of the polygon =ⁿC₂- n
Given,ⁿC₂- n = 44
n (n - 1) / 2 - n = 44
n (n - 3) / 2 = 44
n²- 3n - 88 = 0
(n - 11) (n + 8) = 0
n = 11 or n = - 8
Since n cannot be negative, n = 11
The polygon has 11sides.
THanks

Bharat Bajaj

askiitians faculty
IIT Delhi

ankit singh

Last Activity: 4 Years ago

sidesThe polygon has 11Since n cannot be negative, n = 11n = 11 or n = - 8(n - 11) (n + 8) = 0- 3n - 88 = 0²nn (n - 3) / 2 = 44n (n - 1) / 2 - n = 44- n = 44₂CⁿGiven,- n₂CⁿSo, no. of diagonals of the polygon =of the polygon.sidesOut of these n line segments are₂CNn vertices = joiningNo. of line segments obtained by