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

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

answered Jan 9, 2018 by (-879 points)

Given: In ABC,Dand E are points on the sides AB and AC respectively such that DE || BC. AD = 4cm, AE = 8cm, DB= x-4 and EC=3x-19.
To find: x.
In△ABC. we have DE || BC
Therefon AD/DB = AE/EC [By Thale’s theorem]
4/x-4 = 8/3x-19
4(3x-19)=8(x-4)
12x-76 = 8x-32
4x = 44
x = 11

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