10734 - Triangle Partitioning

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The problem says that:

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A triangle can be divided into two equal triangle by drawing a median on its largest edge


Consider the sample
3 4 5
If I am correct, the 2 small triangles from the first division are (3, 2.5, 2.5) and (4, 2.5, 2.5)
So what is the actual meaning of "equal"???

[little joey]

Their area, but that's completely irrelevant for the problem.

Two triangles (a,b,c): a>=b, b>=c and (a',b',c'): a'>=b', b'>=c' are "similar" (i.e. have the same "style") iff a/a' == b/b' == c/c'.

If you split the two triangles (4,5/2,5/2) and (3,5/2,5/2) again, you get four equal triangles (5/2,2,3/2) (truely equal (congruent) this time), which are similar to the original triangle.

[..]

Thanks, get AC

[Md. Aftabuddin]

[quote="little joey"]Their area, but that's completely irrelevant for the problem.

Two triangles (a,b,c): a>=b, b>=c and (a',b',c'): a'>=b', b'>=c' are "similar" (i.e. have the same "style") iff a/a' == b/b' == c/c'.

If you split the two triangles (4,5/2,5/2) and (3,5/2,5/2) again, you get four equal triangles (5/2,2,3/2) (truely equal (congruent) this time), which are similar to the original triangle.[/quote]

The area is equal in the case of isoceles,equilateral and right tringle but not for general tringle

[andmej]

How can I know when should I stop dividing the smaller triangles?

[rio]

If a triangle has congruity with a triangle which you already got, you could stop dividing it.

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Rio