If LM || AB, AL = 2x - 4, AC = 4x, BM = x - 2 and BC = 2x + 3, then x is ____.

Open in App

Solution

In $△$ ABC,

LM || AB (Given)
$\Rightarrow \frac{C L}{A L} = \frac{C M}{B M}$ [By BPT]
Adding 1 on both sides we get,
$\frac{C L}{A L} + 1 = \frac{C M}{B M} + 1$
$\Rightarrow \frac{C L + A L}{A L} = \frac{C M + B M}{B M}$
$\Rightarrow \frac{C A}{A L} = \frac{C B}{B M}$
$\Rightarrow \frac{4 x}{2 x - 4} = \frac{2 x + 3}{x - 2}$
$\Rightarrow 4 x^{2} - 8 x = 4 x^{2} - 8 x + 6 x - 12$
$\Rightarrow 6 x = 12$
$\Rightarrow x = 2$

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.

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

If $L M ∥ A B, A L = x - 3, A C = 2 x,$ $B M = x - 2, B C = 2 x + 3.$ What is value of AC ?

Join BYJU'S Learning Program