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3 October, 23:55

The total number of sides in two regular polygons is 13, and total number of diagonals is 25. How many sides are in each polygon?

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  1. 4 October, 02:41
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    Let x be the sides of one polygon

    y be the sides of the other polygon

    x + y = 13

    y = 13 - x

    then the formula for the number of polygons is n (n - 3) / 2

    x (x - 3) / 2 + y (y - 3) / 2 = 25

    x (x - 3) / 2 + (13 - x) (13 - x - 3) / 2 = 25

    x (x - 3) / 2 + (13 - x) (10 - x) / 2 = 25

    solve for x

    x = 8

    y = 13 - 8 = 5
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