Question

In a $\Delta ABC,DandE$ are points on the sides $AB$ and $AC$ respectively such that $DE\parallel BC$. If $AD=4x-3,AE=8x-7,BD=3x-1andCE=5x-3$, find the value of $x$.

• A. $1$
• B. $2$
• C. $\frac{1}{2}$
• D. $3$

Answer 1

Answer: (A)

$1$

In $\Delta ABC$, we have
$DE\parallel BC$
$\therefore \frac{AD}{DB}=\frac{AE}{EC}$[By Basic Proportionality Theorem]
$\Rightarrow \frac{4x-3}{3x-1}=\frac{8x-7}{5x-3}$
$\Rightarrow 20x^2-15x-12x+9=24x^2-21x-8x+7$
$\Rightarrow 20x^2-27x+9=24x^2-29x+7$
$\Rightarrow 4x^2-2x-2=0$
$\Rightarrow 2x^2-x-1=0$
$\Rightarrow (2x+1)(x-1)=0$
$\Rightarrow x=1orx=-\frac{1}{2}$
So, the required value of $x$ is $1$.

[$x=-\frac{1}{2}$ is neglected as length can not be negative].