In the following figure, LM $∥$ AB. If AL = x - 3, AC = 2x, BM = x - 2, BC = 2x + 3, then find the value of x.

Open in App

Solution

In $Δ A B C, L M ∥ A B$

$∴ \frac{A L}{L C} = \frac{B M}{M C}$ [By Basic Proportionality Theorem]

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

$\Rightarrow \frac{x - 3}{x + 3} = \frac{x - 2}{x + 5}$

$\Rightarrow (x - 3) \times (x + 5) = (x - 2) \times (x + 3)$

$\Rightarrow x^{2} + 2 x - 15 = x^{2} + x - 6$

$\Rightarrow x = 9$

Suggest Corrections

Similar questions

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

In the given figure $L M | | A B$ . If AL $= x - 3$ , AC $= 2 x$ , BM $= x - 2$ and BC $= 2 x + 3$ , find the value of $x$ .

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 ?

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

In fig., LM $∥$ AB. If AL = $x$ - 3, AC = 2 $x$ , BM = $x$ - 2 and BC = 2 $x$ + 3, Find the value of $x$ .

Join BYJU'S Learning Program