In \(\triangle LMN\), S is a point on side LM and T is a point on side LN such that ST is parallel to MN. If LS \(=4.5\) cm, SM \(=7.5\) cm and LN \(=16\) cm, what is the length of TN?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10 cm
A line drawn parallel to one side of a triangle divides the other two sides in the same ratio (basic proportionality theorem), so \(\frac{LS}{LM}=\frac{LT}{LN}\).
LM \(=\) LS \(+\) SM \(=4.5+7.5=12\) cm
\(\displaystyle\frac{LT}{16}=\frac{4.5}{12}=\frac{3}{8}\)
LT \(\displaystyle=\frac{3}{8}\times16=6\) cm
TN \(=\) LN \(-\) LT \(=16-6=10\) cm
Check: \(\frac{LS}{SM}=\frac{4.5}{7.5}=\frac{3}{5}\) and \(\frac{LT}{TN}=\frac{6}{10}=\frac{3}{5}\), the same ratio.
