Question

A polygon has $27$ diagonals. How many sides it have?

• A. $7$
• B. $8$
• C. $9$
• D. $12$

Answer 1

The correct option is C $9$

We know that to calculate number of diagonals in a polygon we use the formula

$Numberofdiagonals=n\times (n-3)/2$

Using the given value we get:

$27=n\times (n-3)/2$
$n(n-3)=54$
$n^2-3n=54$
$n^2-3n-54=0$
$(n+6)(n-9)=0$

$n=-6$ or $n=9$

Since we are calculating the number of sides it should be positive, therefore the number of sides of a polygon having $27$ diagonals is $9$