Question

A line l intersects the sides PQ and PR of a \(\triangle\) PQR at L and M respectively such that LM || QR. If PL = 5·7 cm, PQ = 15·2 cm and MR = 5·5 cm, then the length of PM (in cm) is :

• A. 3
• B. 1.8
• C. 2.5
• D. 3.3

Answer 1

The Correct Option is D

Using the basic proportionality theorem ($LM \parallel QR$):
\[\frac{PL}{PQ} = \frac{PM}{PR}\]
Substitute the known values:
\[\frac{5.7}{15.2} = \frac{PM}{5.7 + 5.5}\]
\[\frac{5.7}{15.2} = \frac{PM}{11.2}\]
Solve for $PM$:
\[PM = \frac{5.7 \times 11.2}{15.2} = 4.2 \, cm\]