5. Find the value of x for which DE //AB in the right sided figure.

1.	5. Find the value of x for which DE //AB in the right sided figure.
Answer» BASIC PROPORTIONALITY THEOREM (BPT) : If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio. That is also known as Thales theorem. GIVEN:In ∆ABC , DE \|\| ABAD= 3x+19, DC= x+3, BE= 3x+4, EC = x AD /DC = BE/EC [ By Thales theorem(BPT)] 3x+19/x+3 = 3x+4/x(3x+19) × x = (3x+4) × (x+3)3x² + 19x = 3x² + 9x + 4x +123x² + 19x = 3x² + 13x +123x² - 3x² +19x -13x = 126x = 12x = 12/6= 2 x = 2 Hence, the value of x is 2 .

Answer»

BASIC PROPORTIONALITY THEOREM (BPT) : If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio. That is also known as Thales theorem.

GIVEN:In ∆ABC , DE || ABAD= 3x+19, DC= x+3, BE= 3x+4, EC = x

AD /DC = BE/EC

[ By Thales theorem(BPT)]

3x+19/x+3 = 3x+4/x(3x+19) × x = (3x+4) × (x+3)3x² + 19x = 3x² + 9x + 4x +123x² + 19x = 3x² + 13x +123x² - 3x² +19x -13x = 126x = 12x = 12/6= 2

x = 2

Hence, the value of x is 2 .

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