Altitude-altitude-altitude
Construct a triangle with altitudes x, y, and z.
Hint:
Choose a unit segment and construct segments of lengths 1/x, 1/y, and 1/z.
Note that if a triangle has area a/2, and altitudes x, y and z, then its sides are a/x, a/y, and a/z.
Therefore, the constructed triangle is similar to the one we need.
It remains to rescale the constructed triangle so that its altitudes have right sizes.