In triangle PQR, we have <P = 30 degrees, <Q = 60 degrees, and <R=90 degrees. Point X is on line PR such that line QX bisects <PQR. If PQ = 12, then what is the area of triangle PQX$?

Answer 1

since PQR = 60°, PQX = 30°

So triangle PQX is an isosceles triangle with base angles of 30° and base=12

Thus, its altitude is 6/√3 and its area = 36/√3 = 12√3