∵ DE⊥AB AE=BE
∴ △ADB是以AB为底的等腰三角形
S△ABD=2S△ADE
∵ S△ACD/S△ADE = 6/5
∴ S△ACD/S△ABC = 6/16 = 3/8
BC = 8/3*CD AD=BD=5/3CD
∵ AD²=AC²+CD²
(5/3CD)²=8²+CD²
∴ CD = 6 cm
BD= 10 cm AB=8√5
∵ AC/DE=AB/BD
∴ DE = 6*10 / 8√5 = 3√5/2 cm
∵ DE⊥AB AE=BE
∴ △ADB是以AB为底的等腰三角形
S△ABD=2S△ADE
∵ S△ACD/S△ADE = 6/5
∴ S△ACD/S△ABC = 6/16 = 3/8
BC = 8/3*CD AD=BD=5/3CD
∵ AD²=AC²+CD²
(5/3CD)²=8²+CD²
∴ CD = 6 cm
BD= 10 cm AB=8√5
∵ AC/DE=AB/BD
∴ DE = 6*10 / 8√5 = 3√5/2 cm