In the given we are to find the value of X if the length of sides of triangle are given in terms of X by using the properties of similarities

ML Aggarwal Avichal Publication Similarity, chapter 13.2, question no 2b

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Since DE is parllel to BC,by basic proportionality theorem

(AB/DB)=(AC/EC)(2x/x-3)=(2x+3/x-2)

By cross multiplication we get ,

2 x^2 – 4x = 2 x^2 – 3x -9

x = 9