A polygon has number of sides n and diagonals n(n-3)/2 if polygon have 9 diagonals find number of sides
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Answer:
6
Step-by-step explanation:
We're given the formula for the number of diagonals. And we're given the number of diagonals. So equating these, we have
n ( n - 3 ) / 2 = 9
=> n ( n - 3 ) = 18
From here, you can "see" the answer is n = 6, since 18 = 3 x 6.
Otherwise, solve the quadratic:
n² - 3 n - 18 = 0
=> ( n - 6 ) ( n + 3 ) = 0
=> n = 6 or n = -3, but we can't have -3 sides, so we conclude that n = 6.
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