Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
740 views
in Combinations by (48.8k points)
closed by

A convex polygon has 44 diagonals. Find the number of its sides. 

[Hint: Polygon of n sides has (nC2 – n) number of diagonals.]

1 Answer

+1 vote
by (50.2k points)
selected by
 
Best answer

We know that,

Let the number of sides the given polygon have = n

Now,

The number of line segments obtained by joining n vertices = nC2

So, number of diagonals of the polygon = nC– n = 44

n(n - 1)/2 - n = 44

n2 – 3n – 88 = 0

(n – 11) (n + 8) = 0

n = 11 or n = – 8

The polygon has 11 sides.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...