Question

A polygon has 44 diagonals, then the number of its sides are ?
A) 13
B) 9
C) 11
D) 7

Answer 1

Solution :

• Given

No of diagonals = 44

Find the number of its sides.

We know that ;

Diagonals of polygon = $\frac{n(n-3)}{2}$

⇒ $\frac{n(n-3)}{2}$ = 44

⇒ n ( n - 3 ) = 44 × 2

⇒ n ( n - 3 ) = 88

⇒ n² - 3n = 88

⇒ n² - 3n - 88 = 0

⇒ n² - 11n + 8n - 88 = 0

⇒ n ( n - 11 ) + 8 ( n - 11 ) = 0

⇒ ( n - 11 ) ( n + 8 ) = 0

Now,

( n + 8 ) = 0

⇒ n = - 8 [ n cannot be negative ]

And,

( n - 11 ) = 0

⇒ n = 11

Therefore, the number of sides is 11.

Option ( C ) is correct answer.

Answer 2

Check out the above Attachment!!