A polygon has maximum 1325 diagonals. How many vertices does it have?

One Answer on this Question

1. The formula to find number of diagonals (D) given total number of vertices or sides (N) is

   N * (N – 3)

   D = ———–

   2

   Using the formula, we get
   1325 * 2 = N * (N – 3)
   N2 – 3N – 2650 = 0

   Solving the quadratic equation, we get N = 53 or -50

   It is obvious that answer is 53 as number of vertices can not be negative.

   Alternatively, you can derive the formula as triange has 0 diagonals, quadrangel has 2, pentagon has 5, hexagon has 9 and so on……

   Hence the series is 0, 0, 0, 2, 5, 9, 14, …….. (as diagram with 1,2 or 3 vertices will have 0 diagonals).

   Using the series one can arrive to the formula given above.

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