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# Polygons

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The number of diagonals in a certain regular polygon is equal to $$6$$ times the number of sides. How many sides does this polygon have?

Apr 13, 2022

#1
+1384
+1

The formula for diagonals is: $$s(s-3) \over2$$

We now have an equation to solve: $${s(s-3) \over 2} = 6s$$

Simplifying: $$s^2-3s=12s$$

Converting to a quadratic, we get: $$s^2 - 15s = 0$$

We know that $$15s = s^2$$, so there are $$\color{brown}\boxed {15}$$ sides.

Apr 13, 2022

#1
+1384
+1

The formula for diagonals is: $$s(s-3) \over2$$

We now have an equation to solve: $${s(s-3) \over 2} = 6s$$

Simplifying: $$s^2-3s=12s$$

Converting to a quadratic, we get: $$s^2 - 15s = 0$$

We know that $$15s = s^2$$, so there are $$\color{brown}\boxed {15}$$ sides.

BuilderBoi Apr 13, 2022
#2
+122
-1

You seem as if your rly in 10 or higher

Apr 13, 2022
#3
+1384
+1