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

\frac{4}{5}

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\frac{5}{4}

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Solution

The correct option is C 2
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,
$\frac{C L}{A L} + 1 = \frac{C M}{B M} + 1$
$\Rightarrow \frac{C L + A L}{A L} = \frac{C M + B M}{B M}$
$\Rightarrow \frac{C A}{A L} = \frac{C B}{B M}$
$\Rightarrow \frac{4 x}{2 x - 4} = \frac{2 x + 3}{x - 2}$
$\Rightarrow 4 x^{2} - 8 x = 4 x^{2} - 8 x + 6 x - 12$
$\Rightarrow 6 x = 12$
$\Rightarrow x = 2$

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