过A作AD⊥BC于D,过P作PE⊥BC于E,则PE平行于AD
∴S△PBC=PE*BC/2,S△ABC=AD*BC/2
∴S△PBC/S△ABC=PE/AD=BP/BA
由S△PBC=S/4得出BP/BA=1/4即AP/AB=3/4
当P'在AP内取值时,S△P'BC＞S/4