in triangle ABC D and E are points on the sides AB and AC respectively such that DE parallel to BC if AD=4X-3 DB=3X-1 EC=5X-3 FIND

1 thought on “in triangle ABC D and E are points on the sides AB and AC respectively such that DE parallel to BC if AD=4X-3 DB=3X-1 EC=5X-3 FIND”

1. Answer:

   The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

   It is given that AD=4x−38, BD=3x−1, AE=8x−7 and CE=5x−3. Let AC=x

   Using the basic proportionality theorem, we have

   BD

   AD

   =

   AC

   AE

   ⇒

   3x−1

   4x−3

   =

   x

   8x−5

   ⇒x(4x−3)=(3x−1)(8x−5)

   ⇒4x

   2

   −3x=3x(8x−5)−1(8x−5)

   ⇒4x

   2

   −3x=24x

   2

   −15x−8x+5

   ⇒4x

   2

   −3x=24x

   2

   −23x+5

   ⇒24x

   2

   −23x+5−4x

   2

   +3x=0

   ⇒20x

   2

   −20x+5=0

   ⇒5(4x

   2

   −4x+1)=0

   ⇒4x

   2

   −4x+1=0

   ⇒(2x)

   2

   −(2×2x×1)x+1

   2

   =0(∵(a−b)

   2

   =a

   2

   +b

   2

   −2ab)

   ⇒(2x−1)

   2

   =0

   ⇒(2x−1)=0

   ⇒2x=1

   ⇒x=

   2

   1

   Hence, x=

   2

   1

   .

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