Given:
In triangle ACD, BE||CD, AB = 20 cm, BC = 5 cm, CD = 18 cm, AE = 26 cm.
To find:
(a) The length of ED.
(b) The length of BE.
Solution:
In triangle ABE and ACD,
BE||CD, so angle ABE and angles ACD are corresponding angles. So, their measure are equal.
[tex]m\angle ABE=m\angle ACD[/tex] (Corresponding angles)
[tex]m\angle BAE=m\angle CAD[/tex] (Common angle)
Now,
[tex]\Delta ABE\sim \Delta ACD[/tex]
Corresponding sides of similar triangles are proportional.
[tex]\dfrac{AB}{AC}=\dfrac{BE}{CD}=\dfrac{AE}{AD}[/tex]
(a)
[tex]\dfrac{AB}{AC}=\dfrac{AE}{AD}[/tex]
[tex]\dfrac{20}{20+5}=\dfrac{26}{AD}[/tex]
[tex]\dfrac{20}{25}=\dfrac{26}{AD}[/tex]
[tex]0.8=\dfrac{26}{AD}[/tex]
Isolate AD.
[tex]0.8AD=26[/tex]
[tex]AD=\dfrac{26}{0.8}[/tex]
[tex]AD=32.5[/tex]
Now,
[tex]AD=AE+ED[/tex]
[tex]32.5=26+ED[/tex]
[tex]32.5-26=ED[/tex]
[tex]6.5=ED[/tex]
Therefore, the length of ED is 6.5.
(b)
[tex]\dfrac{AB}{AC}=\dfrac{BE}{CD}[/tex]
[tex]\dfrac{20}{25}=\dfrac{BE}{18}[/tex]
[tex]0.8=\dfrac{BE}{18}[/tex]
Multiply both sides by 18.
[tex]14.4=BE[/tex]
Therefore, the length of BE is 14.4.
