已知四边形ABCD,∠B=∠ACD,AB=6,BC=4,AC=5,CD=7.5,求AD的长.
问题描述:
已知四边形ABCD,∠B=∠ACD,AB=6,BC=4,AC=5,CD=7.5,求AD的长.
答
∵AB=6,BC=4,AC=5,CD=7.5,
∴
=AB CD
=BC AC
,4 5
且∠B=∠ACD,
∴△ABC∽△DCA,
∴
=AC AD
=BC AC
,4 5
∴
=5 AD
,4 5
∴AD=
.25 4