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A convex polygon has 44 diagonals. Find the number of its sides. |
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Answer» Answer: If you are talking about an n-sided CONVEX polygon, then its number of diagonals are given by nC2 - n; and if nC2 - n = 44 (given), then ½ n (n - 1) - n = 44 n^2 - n - 2 n = 88 n^2 - 3 n - 88 = 0 Solving the quadratic, we have n^2 - 11 n + 8 n - 88 = 0 (n - 11) (n + 8) = 0 Since, n = -8 is not applicable, hence the polygon in QUESTION must have 11 number of sides to it. Hope it helps |
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