Point D is the foot of the altitude from the right angle, so CA must be the geometric mean of CD and CB.

(CB)(CD) = CA²

5(CD) = 4²

CD = 16/5

Point E is the midpoint of CB, so CE must be half of CB.

CE = CB/2

CB = 5/2

**DE **

= CD - CE

= 16/5 - 5/2

= 32/10 - 25/10

= 7/10