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 ~-)