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Question

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

In ΔABC,LMAB

ALLC=BMMC [By Basic Proportionality Theorem]

x32x(x3)=x2(2x+3)(x2)

x3x+3=x2x+5


(x3)×(x+5)=(x2)×(x+3)


x2+2x15=x2+x6


x=9




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Basic Proportionality Theorem
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