In triangle abc, DE is parallel to BC such that AD = x+3, DB =2x-3, AE = x-2 and AC = 3x+3 ; find the value of x.
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Answer:
The value of x is 2.
Step-by-step explanation:
By Basic Proportionality Theorem or Thales Theorem :
If a line is parallel to a side of a triangle which intersects the other side into two distinct points, then the line divides those sides in proportion.
Therefore, AD/DB =AE/EC
x+2 / 3x+16 = x / 3x+5
x(3x+16) = (x+2) / (3x+5)
3x^2 + 16 = 3x^2 + 5x +6x + 10
16x = 11x + 10
16x - 11x = 10
5x = 10
x = 10/5
x = 2
, 2.
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