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
1.0k views
in Permutations by (26.7k points)
closed by

A polygon has 35 diagonals. Find the number of its sides.

1 Answer

+1 vote
by (26.1k points)
selected by
 
Best answer

Let n be the number of sides of a polygon and D be the number of diagonals of that polygon 

We know that, D = \(n_{c_2}\) -  n = \(\frac{n(n-3)}{2}\) 

∴ 35 = \(\frac{n^2-3n}{2}\) 

⇒ n2 − 3n − 70 = 0 

⇒ (n − 10)(n + 7) = 0 

⇒ n = 10, −7 

Since, sides cannot be negative, therefore n = 10. 

Hence, polygon is a decagon.

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.

...