# <span lang="EN-US

No. of diagonals = n(n - 3) = 2 × 65

n2 - 3n = 130

n2 - 3n - 130 = 0

Performing factorization we get:

n2 - 13n + 10n - 130 = 0

n(n - 13) + 10(n - 13) = 0

(n + 10)(n - 13) = 0

n = 13, - 10

Since no. of sides cannot be negative so

No. of Sides = 13

When No. of Diagonals is 50

n(n - 3) = 50 × 2

n2 - 3n - 150 = 0

Discriminant = (9 - 4 × 1 × ( - 150)) = 609

Since 609 is not a perfect square so n can never be a whole number.

Hence 50 diagonals are not possible

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

<span lang="EN-USAP- Mathematics

<span lang="EN-USAP- Mathematics

<span lang="EN-USAP- Mathematics

<span lang="EN-USAP- Mathematics

<span lang="EN-USAP- Mathematics

<span lang="EN-USAP- Mathematics

<span lang="EN-USAP- Mathematics

<span lang="EN-USAP- Mathematics

<span lang="EN-USAP- Mathematics

<span lang="EN-USAP- Mathematics