Question

If in $△$ABC, DE $\parallel$ BC and $AD=4x-3$,$AE=8x-7$,$BD=3x-1$ and $CE=5x-3$ then the value of $x$ is :

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is D $1$

According to equation,
$DE\parallel BC$
$\therefore \frac{AD}{BD}=\frac{AE}{CE}$ (By B.P. Theorem)
or, $\frac{4x-3}{3x-1}=\frac{8x-7}{5x-3}$
or, $24x^2-29x+7=20x^2-27x+9$
or, $4x^2-2x-2=0$
or, $2x^2-x-1=0$
Again, $2x^2-x-1=0$
or, $2x^2-2x+1=0$
or, $2x(x-1)+1(x-1)=0$
or, $(2x+1)(x-1)=0$
$\therefore x=-\frac{1}{2},1$
Hence obtion (D) is correct answer