In triangle ABC, LM parallel to BC, BL= x - 3, AB = 2x, CM = x-2 and AC =2x + 3. Find the value of x
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Answer:
Hiii
Step-by-step explanation:
In ∆ABC , LM//AB
AL = x - 3 , AC = 2x ,
BM = x - 2 , and BC = 2x + 3 ,
Solution :
In ∆ABC ,LM// AB
=> AL/LC = BM/MC
[ Thales theorem ]
( x - 3 )/[ 2x - ( x - 3 )] = (x-2)/[ (2x+3)-(x-2)]
=> (x-3)/(x+3) = ( x-2 )/(x+5)
=> (x-3)(x+5) = ( x-2)(x+3)
=> x² + 2x - 15 = x² + x - 6
=> 2x - 15 = x - 6
=> 2x - x = 15 - 6
x = 9
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