QQuestion
In ΔABC, L and M are two points on the sides AC and BC respectively such that LM || AB and AL are (x – 2) units, AC = 2x + 3 units, BM = (x – 3) units and BC = 2x units. Determine the value of x.
✓Answer
AL = x – 2
AC = 2x + 3
BM = x – 3
BC = 2x
ΔMCL ∼ ΔBCA
\text{AL}\over \text{AC} = \text{BM}\over \text{BC}
or, \text{x - 2}\over \text{2x + 3} = \text{x - 3}\over \text{2x}
or, 2x² – 4x = 2x² – 6x + 3x – 9
or, – 4x + 6x – 3x =-9
or, x = 9
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