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Does a polygon ever have more diagonals than sides? - Answers

The number of diagonals for a shape with x sides is (x²-3x)/2 The number of sides is x You want to know if x is ever less than (x²-3x)/2 or else (x²-3x)/2 - x > 0 (x² - 3x) / 2 - x > 0 (x² - 3x)/2 - (2x)/x > 0 x² - 3x - 2x > 0 x² - 5x > 0 x(x-5)>0 This only true if x<0 or x>5, and since a polygon cannot have less than 2 sides, x<0 is meaningless. This means that if x<5 then the number of diagonals is less than the number of sides, equal for x=5, and more for x>5. ■



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Does a polygon ever have more diagonals than sides? - Answers

https://math.answers.com/math-and-arithmetic/Does_a_polygon_ever_have_more_diagonals_than_sides

The number of diagonals for a shape with x sides is (x²-3x)/2 The number of sides is x You want to know if x is ever less than (x²-3x)/2 or else (x²-3x)/2 - x > 0 (x² - 3x) / 2 - x > 0 (x² - 3x)/2 - (2x)/x > 0 x² - 3x - 2x > 0 x² - 5x > 0 x(x-5)>0 This only true if x<0 or x>5, and since a polygon cannot have less than 2 sides, x<0 is meaningless. This means that if x<5 then the number of diagonals is less than the number of sides, equal for x=5, and more for x>5. ■



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https://math.answers.com/math-and-arithmetic/Does_a_polygon_ever_have_more_diagonals_than_sides

Does a polygon ever have more diagonals than sides? - Answers

The number of diagonals for a shape with x sides is (x²-3x)/2 The number of sides is x You want to know if x is ever less than (x²-3x)/2 or else (x²-3x)/2 - x > 0 (x² - 3x) / 2 - x > 0 (x² - 3x)/2 - (2x)/x > 0 x² - 3x - 2x > 0 x² - 5x > 0 x(x-5)>0 This only true if x<0 or x>5, and since a polygon cannot have less than 2 sides, x<0 is meaningless. This means that if x<5 then the number of diagonals is less than the number of sides, equal for x=5, and more for x>5. ■

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      The number of diagonals for a shape with x sides is (x²-3x)/2 The number of sides is x You want to know if x is ever less than (x²-3x)/2 or else (x²-3x)/2 - x > 0 (x² - 3x) / 2 - x > 0 (x² - 3x)/2 - (2x)/x > 0 x² - 3x - 2x > 0 x² - 5x > 0 x(x-5)>0 This only true if x<0 or x>5, and since a polygon cannot have less than 2 sides, x<0 is meaningless. This means that if x<5 then the number of diagonals is less than the number of sides, equal for x=5, and more for x>5. ■

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