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.  

Answer 1

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