Question

In triangle ABC ,DE parallel BC,IF AD =x+2, DB=3x+16, AE=x , EC= 3x+5,then find the x. ???????????

Answer 1

Answer:

Step-by-step explanation:

Answer 2

By Basic Proportionality Theorem or Thales Theorem :

If a line is parallel to a side of a triangle which intersects the other sides 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 + 16x = 3x^2 +5x + 6x +10

= 16x = 11x + 10

= 16x - 11x = 10

= 5x = 10

= x= 2

Hence value of x is 2.