Question

if a regular polygon has 104 diagonals then the no of sides are?

Answer 1

Hello Dear.

Here is the answer---

Number of Diagonals in the Regular Polygon = 104.

∵ Number of Diagonals = (n - 3)n ÷ 2
Where, n = number of sides in the polygon.

∴ 104 × 2 = n(n - 3)
⇒ n² - 3n = 208
⇒ n² - 3n - 208 = 0

Splitting the Middle Term,
⇒ n² - 16n + 13n - 208 = 0
⇒ n(n - 16) + 13(n - 16) = 0
⇒ (n - 16)(n +13) = 0
⇒ n = 16 and n = -13

∵ Number of sides cannot be -13.
∴ Rejecting n = -13.

Hence, number of sides in the Regular Polygon is 16.


Hope it helps.