In the given figure, the value of x for which DE || AB is


In the given figure, the value of x for which DE || AB is

(a) 4
(b) 1
(c) 3
(d) 2


Given: In ∆ABC,  DE || AB.

To find: the value of x

According to basic proportionality theorem if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.

In ∆ABC,  DE || AB


$\frac{x+3}{3 x+19}=\frac{x}{3 x+4}$

$(x+3)(3 x+4)=(x)(3 x+19)$

$3 x^{2}+4 x+9 x+12=3 x^{2}+19 x$

$19 x-13 x=12$

$6 x=12$


Hence we got the result $(d)$.

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