It was made a serie of stick's triangles following the sequence in the figure. One of these triangles was built with 135 sticks. How many sticks form the side of this triangle?

Guest Jan 7, 2020

#1**+1 **

You'll note that it takes three sticks to make a triangle. So your structure with 135 sticks must comprise 45 individual triangles, by "individual" meaning only the ones with a point at the top. For example, in the illustration, the center one contains 3 individual triangles.

So, if there are 45 triangles total, that means the bottom row must contain 9 triangles. If the bottom has 9 triangles, then so do both sides, and therefore there will be **9** sticks along the side.

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Guest Jan 7, 2020