My Math Forum divide a triangle in two parts with the same area

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 February 5th, 2010, 01:06 AM #1 Newbie   Joined: Nov 2009 Posts: 12 Thanks: 0 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
 February 6th, 2010, 05:29 AM #2 Senior Member   Joined: Jan 2009 From: Japan Posts: 192 Thanks: 0 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?
 February 7th, 2010, 04:33 AM #3 Newbie   Joined: Nov 2009 Posts: 12 Thanks: 0 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.
 February 9th, 2010, 02:18 PM #4 Newbie   Joined: Dec 2009 Posts: 7 Thanks: 0 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.
 February 9th, 2010, 04:25 PM #5 Global Moderator   Joined: Dec 2006 Posts: 20,306 Thanks: 1976 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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