如图,矩形ABCD中,AB=3,AD=12,点M分BC为BM:MC=1:2.则点D到直线AM的距离DE=_.
问题描述:
如图,矩形ABCD中,AB=3,AD=12,点M分BC为BM:MC=1:2.则点D到直线AM的距离DE=______.
答
设DE和BC交于F,
∵AB=3,AD=12,BM:MC=1:2
∴BM=4,CM=8,
∴AM=
=5,
32+42
∵AD∥BC,
∴∠AMB=∠MAD,
又∵∠B=∠E=90°,
∴△ABM∽△AED,
∴
=AD AM
,DE AB
∴DE=7.2.