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February 5th, 2010, 12:06 AM   #1
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divide a triangle in two parts with the same area

hello,

as written in the subject, i have to find a solution for this problem:

divide a triangle by a straight line of minimal length in two parts with the same area.

thank you for any piece of advice

marten
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February 6th, 2010, 04:29 AM   #2
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Re: divide a triangle in two parts with the same area

There is not a unique solution to this problem, at least for equilateral triangles and possibly for others.

Do you have more information on the restrictions?

In particular, should the cut leave two triangles, or is a triangle and a quadrilateral acceptable?
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February 7th, 2010, 03:33 AM   #3
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Re: divide a triangle in two parts with the same area

for the triangle there are no restrictions, so it can be any triangle.
the cut should leave two "parts", without any restrictions about their shape, so the result can also be a quadrilateral.
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February 9th, 2010, 01:18 PM   #4
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Re: divide a triangle in two parts with the same area

It works for any triangle, and there are many solutions to the problem, for instance if you think in the area of a triangle, you will probably think in A = b*h /2, so one solutions is taking any one of the medians, you will have that the area of any of the triangles left is A= b*h /2, with b= b/2 and therefore A= A /2.
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February 9th, 2010, 03:25 PM   #5
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If the medians have different lengths, one is shortest, but one can also consider whether there is a still shorter line that divides the triangle into a triangle and quadrilateral of equal area.
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