Question

A polygon has 54 diagonals then the sides of the polygon is

Answer 1

Answer:

Thus for given number of 54 diagonals, the number of sides are 12 ( Arrived at after substituting values for diagonals in the above mentioned formulae and simplifying.) The polygon which has 12 sides is called Dodecagon.

Answer 2

$\bold\green{Number\:of\:sides}$= 12 sides.

EXPLANATION:

The number of diagonals of a polygon of n sides are given by

⇛$\frac{n(n-3)}{2}$

Since, there are 54 diagonals.

$⇛ \frac{n(n - 3)}{2} = 54 \\ ⇛n(n - 3) = 108 \\ ⇛ {n}^{2} - 3n - 108 = 0 \\ ⇛ {n}^{2} - 12n + 9n - 108 = 0 \\ ⇛n(n - 12) + 9(n - 12) = 0\\ ⇛(n + 9)(n - 12) = 0 \\ ⇛n = - 9(neglect) \: and \: 12$

So, the polygon has 12 sides and it is called $\bold\red{Dodecagon}$.