For DE ⊥ AB and DF ⊥ AC, the vertical feet are E and F respectively. Because AD is the bisector of the angle BAC, DE=DF (the distances of points on the bisector of the angle are equal).

S△ABD= 1/2 *AB*DE ①

S△ACD= 1/2*AC*DF ②

①/② Available

S△ABD:S△ACD=AB:AC

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