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Question
In the given figure, if ∠ADE = ∠B, show that ΔADE ~ ΔABC. If AD = 3.8cm, AE = 3.6cm, BE = 2.1cm and BC = 4.2cm, find DE.
Solution
Given :
∠𝐴𝐷𝐸= ∠𝐴𝐵𝐶 𝑎𝑛𝑑 ∠𝐴= ∠𝐴
Let DE be X cm
Therefore, by AA similarity theorem, Δ ADE - Δ ABC
⇒ `(AD)/(AB)=(DE)/(BC)`
⇒ `3.8/(3.6+2.1)=x/4.2`
⇒` x=(3.8xx4.2)/5.7=2.8`
Hence, DE = 2.8 cm 
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