设AC与BD相交于O,则S四边形ABCD=SΔABC+SΔADC=1/2AC*OB+1/2AC*OD=1/2AC(OB+OD)=1/2AC*BD=1/2AC(10-AC)=-1/2(AC-10AC)=-1/2(AC-5)+25/2∴当AC-5=0,即AC=5时,S最大=25/2,此时AC=BD=5.
