Choose a unit segment and construct segments of lengths 1/x, 1/y, and 1/z. [br][br]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.[br]Therefore, the constructed triangle is similar to the one we need.[br][br]It remains to rescale the constructed triangle so that its altitudes have right sizes.[br]