$If LM || AB, AL = 2 x - 4, AC = 4 x,$ $BM = x - 2 and BC = 2 x + 3 with x > 0,$ $then find the value of x .$ $[3 Marks]$

[3 Marks]

Open in App

Solution

$In △ ABC,$

$Given : L M | | A B$

$\Rightarrow \frac{C L}{A L} = \frac{C M}{B M}$ $(By basic proportionality theorem)$ $[1 Mark]$

$By adding 1 on both the sides we get,$
$\Rightarrow \frac{C L}{A L} + 1 = \frac{C M}{B M} + 1$

$\Rightarrow \frac{C L + A L}{A L} = \frac{C M + B M}{B M}$

$\Rightarrow \frac{A C}{A L} = \frac{B C}{B M}$ $[1 Mark]$

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

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

$\Rightarrow 6 x = 12$

$\Rightarrow x = 2 units$ $[1 Mark]$

Suggest Corrections

Similar questions

If LM || AB, AL = 2x - 4, AC = 4x,

BM = x - 2 and BC = 2x + 3 with x > 0,

then find the value of x.

[3 Marks]

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

If LM $∥$ AB, AL=x-3, AC=2x, BM=x-2, BC=2x+3. What is value of AC?

Join BYJU'S Learning Program