Question

In the figure given, for what value of x is DE $\parallel$ BC?

• A. $1$
• B. $3$
• C. $0$
• D. $2$

Answer 1

The correct option is D $2$

Given that $DE\parallel BC$

Using the information given in the passage, if $DE||BC$

Then $\frac{AD}{BD}=\frac{AE}{EC}$

$\Rightarrow \frac{x}{3x+4}=\frac{x+3}{8x+9}$

$\Rightarrow x(8x+9)=(x+3)(3x+4)$

$\Rightarrow 8x^2+9x=3x^2+13x+12$

$\Rightarrow 5x^2-4x-12=0$

$\Rightarrow 5x^2-10x+6x-12=0$

$\Rightarrow (x-2)(5x+6)=0$

$\Rightarrow x=2$