LM || AB if AL = X-3 AC = 2X BM = X-2 and BC = 2X + 3 FIND THE VALUE OF X.

LM || AB if AL = X-3 AC = 2X BM = X-2 and BC = 2X + 3 FIND THE VALUE O

1.	LM \|\| AB if AL = X-3 AC = 2X BM = X-2 and BC = 2X + 3 FIND THE VALUE OF X.
Answer» We have, AL = x - 3, AC = 2x, BM = x - 2 and BC = 2x + 3, and we need to find the value of x.In\xa0{tex}\\Delta{/tex}ABC, we have{tex}L M \\\| A B{/tex}{tex}\\therefore \\quad \\frac { A L } { L C } = \\frac { B M } { M C }{/tex}\xa0[By Thaley\'s Theorem]{tex}\\Rightarrow \\quad \\frac { A L } { A C - A L } = \\frac { B M } { B C - B M }{/tex}{tex}\\Rightarrow \\quad \\frac { x - 3 } { 2 x - ( x - 3 ) } = \\frac { x - 2 } { ( 2 x + 3 ) - ( x - 2 ) }{/tex}{tex}\\Rightarrow \\quad \\frac { x - 3 } { x + 3 } = \\frac { x - 2 } { x + 5 }{/tex}{tex} \\Rightarrow{/tex}\xa0(x - 3) (x + 5) = (x - 2) (x + 3){tex} \\Rightarrow{/tex}\xa0x2 + 2x -15 = x2 + x - 6{tex} \\Rightarrow{/tex}\xa0x = 9