Question

A polygon of n sides has n(n-3)/2 diagonals . If a polynomial has 9 diadonals find the no of sides of the polygon

Answer 1

Answer:

6

Step-by-step explanation:

n(n - 3) / 2 = 9

n(n - 3) = 9 × 2

n² - 3n = 18

n² - 3n - 18 = 0

n² + 3n - 6n - 18 = 0

n(n + 3) - 6(n + 3) = 0

(n + 3)(n - 6) = 0

∴ n = -3       ;       n = 6

As no. of polygons is asked, n ≠ -3.

∴ n = 6

So the polygon is a hexagon.

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