Secting Equilateral Triangle

Geometry Level 1

Is it possible to divide a non-degenerate equilateral triangle into 5 parts of equal area (not necessarily connecting)?

Bonus: What about 5 equal triangles?

No, never. Yes, it is possible.

Michael Huang by Michael Huang , 29, USA

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1 solution

Michael Huang
Aug 11, 2017

This shows how it is possible to divide into equal parts, but not in congruent triangular connected parts.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

You can divide them in the connecting pieces by dividing the triangle's side in the ratio 1 : 2 : 3 : 2 : 5 . 1 : \sqrt 2 : \sqrt 3 : 2 : \sqrt 5. Equal and equilateral 5 5 pieces are impossible.

Vishwash Kumar ΓΞΩ - 3 years, 10 months ago

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Exactly the point! You said it! :)

Michael Huang - 3 years, 9 months ago

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Really I gave such a boring advice above. Mark 5 5 points on the base of the triangle such that it divides the triangle's sides in 5 5 equal parts. Now join the vertex above to all these points ;)

Vishwash Kumar ΓΞΩ - 3 years, 9 months ago

Wow! Soooooooo colourful!

Annie Li - 3 years, 9 months ago

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