According to pythagorean theorem, that is, AB 2-AM 2 = BC 2-CM 2.

That is,100-x2 =169-(13-x) 2 solution, x=50/ 13.

bm^2=bc^2-cm^2= 120/ 13

Because d is the midpoint of AB, DE⊥AC,

Because BM⊥AC,

So △ADE is similar to△ △ABM.

So DE= 1/2BM=60/ 13.

(except for the two-year senior high school entrance examination, mathematics is still very friendly ~-)