If A Polygon Has 119 Diagonals, How Many Sides Does It Have? I Know The Formula To Find Out Diagonals, D=s(s-3)/2 S=sides D=diagonals How Do I Rewrite That Equation To Give Me Numbers Of Diagonals? Thanks!

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Oddman Profile
Oddman answered
You probably want to rewrite the equation to give you the number of sides.

d = s(s-3)/2
2d = s(s-3)
s2 -3s -2d = 0    (this is the standard form of a quadratic equation. You use the quadratic formula to solve it.)

s = (3 ±√(32 - 4*(1)(-2d)))/(2*(1))
s = (3 +√(9+8d))/2    (probably only the positive root is useful)

For d = 119, this is
s = (3 +√(9+8*119))/2 = (3+√961)/2 = (3+31)/2 = 34/2 = 17

Your polygon has 17 sides.

Check
d = 17(17-3)/2 = 17*14/2 = 17*7 = 119
Anonymous Profile
Anonymous answered
How many triangles can be made if you draw all possible diagonals from a single vertex on a 50- sided polygon?

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