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

(2 Marks)

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Solution

It's given LM $∥$ AB,
So, $\frac{C L}{C A} = \frac{C M}{C B}$ [By Basic Proportionality Theorem]
$\frac{(x - 3)}{2 x} = \frac{(x - 2)}{(2 x + 3)} (1 M a r k)$

$(x - 3) (2 x + 3)$ = $(x - 2) 2 x$

$2 x^{2} - 3 x - 9$ = $2 x^{2} - 4 x$
$x = 9 u n i t s (1 M a r k)$
$S o, A C = 2 x = 18 u n i t s$

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