Based on geometry, Triangle

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What is the least possible length of a line segment that cuts a triangle with sides 3,4,5 in to two geometric figures having equal area?

1

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Hints:

  1. Among triangles of equal area with a given angle between two sides, the isosceles triangle has the least possible side opposite to the angle.

  2. Among isosceles triangles of equal area, the triangle with the smallest angle has the least possible side opposite to the angle.

Applying the above considerations and some simple trigonometry you should end up with the answer "2".