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=______.

设DE和BC交于F,
∵AB=3,AD=12,BM:MC=1:2
∴BM=4,CM=8,
∴AM=

32+42
=5,
∵AD∥BC,
∴∠AMB=∠MAD,
又∵∠B=∠E=90°,
∴△ABM∽△AED,
AD
AM
DE
AB

∴DE=7.2.