连接CP
∵∠ACB=90,AC＝6,BC＝8
∴S△ABC＝AC×BC/2＝6×8/2＝24
∵PM⊥AC,PN⊥BC
∴S△APC＝AC×PM/2＝6×PM/2＝3PM,S△BPC＝BC×PN/2＝8×PN/2＝4PN
∴S△ABC＝S△APC+ S△BPC
∴3PM+4PN＝24
∵PM＝PN
∴7PM＝24
∴PM＝24/7