Question

In the given figure, LM AB  . If AL = x – 3, AC = 2x, BM = x – 2 and BC = 2x + 3. Find the value

of x.
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Answer 1

Step-by-step explanation:

In triangle ABC

LM ll AB

By basic proportionality theorem (i.e. B.P.T.)

CL/LA = CM/MB

By using 'componendo property'

CL+LA / LA = CM+MB/MB

CA/LA = BC/MB.... (C-L-A) & (C-M-B)

..... (1)

Putting value in equation (1)

2x/x-3 = 2x+3/x-2

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

2x^2-4x = 2x^2 -6x +3x.-9

Cancel the same terms on both sides

-4x = - 6x+3x-9

-4x = - 3x - 9

-4x + 3x = - 9

-x = - 9

i. e. X= 9

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