Question

What value of $x$ will make $DE\parallel AB$ in the given figure$?$

• A. $x=3$
• B. $x=2$
• C. $x=1$
• D. $x=5$

Answer 1

The correct option is B $x=2$

By the converse of basic proportionality theorem, if $\frac{CD}{DA}=\frac{CE}{EB},$ then $DE\parallel AB$
$\Rightarrow$ $\frac{x+3}{8x+9}=\frac{x}{3x+4}$
$\Rightarrow$ $(3x+4)(x+3)=x(8x+9)$
$\Rightarrow$ $3x^2+13x+12=8x^2+9x$
$\Rightarrow$ $5x^2-4x-12=0$
$\Rightarrow$ $5x^2-10x+6x-12=0$
$\Rightarrow$ $5x(x-2)+6(x-2)=0$
$\Rightarrow$ $(5x+6)(x-2)=0$
$\Rightarrow$ $x=\frac{-6}{5}$ or $2$
Since, $x$ cannot be negative, $x=2.$