The length of ED is 6.5cm.
The length of BE is 14.4 cm.
In ΔACD
BE ∥ CD
In ΔACD and ΔABE
BE ∥ CD
∠ACD =∠ABE (corresponding angles)
∠ADC = ∠AEB (corresponding angles)
∠A = ∠A (common angle)
∴ΔACD ∼ ΔABE
So, The corresponding sides are in proportion.
Now, find ED
[tex]\frac{AB}{BC}=\frac{AE}{ED}\\ED=AE(\frac{BC}{AB}) \\ED=26(\frac{5}{20} \\ED=6.5 cm[/tex]
Now, find BE
[tex]\frac{AB}{AC} =\frac{BE}{CD} \\BE=CD(\frac{AB}{AC})\\BE=18(\frac{20}{25})\\BE=14.4 cm[/tex]
Therefore, the length of ED is 6.5cm and the length of BE is 14.4 cm.
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