Answer:
AB = 5.2 cm , ED = 5 cm
Step-by-step explanation:
Δ ABE and Δ ACD are similar by the AA postulate
Then the ratios of corresponding sides are in proportion , that is
(a)
[tex]\frac{AB}{AC}[/tex] = [tex]\frac{BE}{CD}[/tex] , substitute values
[tex]\frac{AB}{11.7}[/tex] = [tex]\frac{6}{13.5}[/tex] ( cross- multiply )
13.5 × AB = 70.2 ( divide both sides by 13.5 )
AB = 5.2 cm
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(b)
[tex]\frac{AE}{AD}[/tex] = [tex]\frac{BE}{CD}[/tex] , substitute values
[tex]\frac{4}{AD}[/tex] = [tex]\frac{6}{13.5}[/tex] ( cross- multiply )
6 × AD = 54 ( divide both sides by 6 )
AD = 9
Then
ED = AD - AE = 9 - 4 = 5 cm
