Question

$\text{If LM || AB, AL = 2x - 4, AC = 4x,}\text{BM = x - 2 and BC = 2x + 3 with x >0,}\text{then find the value of x.}$

Answer 1

$\text{In}△\text{ABC,}$

$\text{Given :}LM||AB$

$\Rightarrow \frac{CL}{AL}=\frac{CM}{BM}\text{(By basic proportionality theorem)}$

$\text{By adding 1 on both the sides we get,}$
$\Rightarrow \frac{CL}{AL}+1=\frac{CM}{BM}+1$

$\Rightarrow \frac{CL+AL}{AL}=\frac{CM+BM}{BM}$

$\Rightarrow \frac{AC}{AL}=\frac{BC}{BM}$

$\Rightarrow \frac{4x}{2x-4}=\frac{2x+3}{x-2}$

$\Rightarrow 4x^2-8x=4x^2-8x+6x-12$

$\Rightarrow 6x=12$

$\Rightarrow x=2\text{units}$