What values of x will make D E | A B in the figure? - Vidyadip

MCQ

What values of $x$ will make $D E \| A B$ in the figure?

A
$1$
✓
$2$
C
$3$
D
$4$

✓

Answer

Correct option: B.

$2$

$D E \| A B$ if $\frac{C D}{D A}=\frac{C E}{E B}$
$($By converse of Thales theorem$)$
$\therefore \frac{x+3}{3 x+19}=\frac{x}{3 x+4}$
$\Rightarrow \quad(x+3)(3 x+4)=x(3 x+19)$
$\Rightarrow 3 x^2+4 x+9 x+12$
$=3 x^2+19 x$
$\Rightarrow 12=6 x $
$\Rightarrow x=2$
Hence, $x=2$ will make $D E \| A B$.

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