Three equal area triangles:
3-4-5 reference triangle case
Problem
In the 3-4-5 triangle ABC,
three (yellow) triangles
are of the same area s = 1/5 area of triangle ABC.
Construct the points D, E, F!
Answer:
For any s < 1/4 ,
(sure s can not be larger than 1/4):
CD = 3/2 [1-sqrt(1 - 4s)],
AE = 2 [1-sqrt(1 - 4s)],
BF = 5/2 [1-sqrt(1 - 4s)].
For s = 1/5 construction is trivial.