Minimal perimeters of triangles with fixed area and foot.

Triangle with the same area can have different perimeters. In this project we are exploring the question of when those perimeters are as small as possible. With no further conditions, the answer to this question is known: the minimal perimeter is obtained by an equilateral triangle. We can explore the question under the condition that location of the height is fixed. In this case the minimal perimeter can be obtained by variety of different triangle types. We want to know which type of a triangle has minimal perimeter based on the location of the height