Posted by **Mark** on Monday, July 15, 2013 at 4:57pm.

Brilli the ant has a block of cheese that is in the shape of an equilateral triangle. She is hosting a party, and has invited her two-legged house mates. She insists that all of her guests get a piece of cheese that is in the shape of an isosceles triangle. What is the maximal number N such that she cannot split the equilateral triangle block of cheese into N non-degenerate isosceles triangles?

- Math -
**MathMate**, Monday, July 15, 2013 at 6:07pm
She cannot subdivide the equilateral triangle into 2 isosceles triangles. This is the smallest N which is impossible.

She can subdivide it into 3 congruent isosceles triangles by joining the centroid with each of the vertices. Each triangle is then 30-30-120 as angles.

Each of the 30-30-120 triangles can in turn be subdivided into 3 isosceles triangles with angles 60-60-60, and 30-30-120, thus adding two more triangles.

So the next possible N are then 5, 7, 9.

Since each of the smaller 30-30-120 triangles can again be subdivided, indefinitely, we conclude that the original equilateral triangle can be subdivided into odd N above 1. Even N are therefore not possible. Thus there is no maximum number N, since N->∞, as long as N=2k, where k∈integers.

- Math -
**MysteriousPerson**, Thursday, July 18, 2013 at 5:37pm
MathMate, I would disagree with you because 4 triangles are possible. We can break up the equilateral triangle to 4 different equilateral triangles.

## Answer This Question

## Related Questions

- Math - Brilli the ant has a block of cheese that is in the shape of an ...
- physics - Three ants are sitting on the vertices of equilateral triangle of side...
- Math - Phil bought a block of cheese in the shape of a rectangular prism ...
- Math - Fractions - Mary has invited all her friends and all the students in her ...
- MATH! - how do you solve this plz show me how you do this 1. on her last three ...
- Geometry - Can anybody help me with this word problem? A homeowner, who loves ...
- Math - Lenlen cut a rectangular block of cheese into cubes with an edge of 3cm ...
- math - lenlen cut a rectangular block of cheese into cubes with an edge of 3cm. ...
- math - Brilli the ant is considering the complexities of a 5-dimensional ...
- math - A wire of length 4 m is cut in two parts and the first part is bent in ...

More Related Questions