As shown in the figure: the side length of equilateral △ ABC is 5, ad is the middle line on BC side, M is the moving point on ad, e is a point on AC side. If AE = 2, the minimum value of EM + cm is________ The title says that the length of the side is 5. I can't find it on the Internet. I want the mid-term exam tomorrow

As shown in the figure: the side length of equilateral △ ABC is 5, ad is the middle line on BC side, M is the moving point on ad, e is a point on AC side. If AE = 2, the minimum value of EM + cm is________ The title says that the length of the side is 5. I can't find it on the Internet. I want the mid-term exam tomorrow

Because equilateral triangles are axisymmetric
So we are looking at the shortest distance
Because ad is the middle line,
An equilateral triangle
So B and C are symmetric with respect to the line ad,
Connect ad to point M,
Be = MB + me = MC + me, i.e. m is the point, CE = 3, BC = 5
In the right triangle EHC, EC = 3, angle c = 60
So HC = 3 / 2, eh = 3 / 2 times root 3. So BH = 7 / 2
So from Pythagorean theorem: be = root 19