Q20 of 56 Page 6

In a Δ ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 4 cm, AE = 8 cm, DB = x – 4
and EC = 3x – 19, find x.

 


Given: In Δ ABC, D and E are points on the sides AB and AC respectively such that DE || BC. AD = 4 cm, AE = 8 cm, DB = x - 4 and EC = 3x - 19. 
To find: x.
In Δ ABC, we have DE || BC
Therefore  [By Thale's theorem]

4(3x - 19) = 8(x - 4)
12x – 76 = 8x – 32
4x = 44
x = 11

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