Q. 44.4( 20 Votes )

In the given figure, if ADE = B, show that ΔADE ~ ΔABC. If AD = 3.8 cm, AE = 3.6 cm, BE= 2.1 cm and BC = 4.2 cm, find DE.


Answer :

Given is that ADE = B

From the diagram clearly, EAD = BAC [ they are common angles]


Now, since two of the angles are correspondingly equal. Then by AA similarity criteria, we can say


∆ADE ∆ABC


Further, it’s given that


AD = 3.8 cm


AE = 3.6 cm


BE = 2.1 cm


BC = 4.2 cm


DE =?


To find AB, we can express it in the form AB = AE + BE = 3.6 + 2.1


AB = 5.7


So for the condition that ∆ADE ∆ABC,



Substituting given values in the above equation,




DE = 2.8


Thus, DE = 2.8 cm


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