Question

P and Q are points on sides AB and AC respectively of $\Delta ABC$. If AP = 3 cm, PB = 6 cm, AQ = 5 cm and QC =I 10 cm, then BC.

• A. $PQ$
• B. $2PQ$
• C. $3PQ$
• D. $4PQ$

Answer 1

Answer: (C)

$3PQ$

$\frac{AP}{PB}=\frac{AQ}{QC}$

$\Rightarrow \frac{3}{6}=\frac{5}{10}=\frac{1}{2}$

$\therefore PQ\parallel BC$

Also,

$△APQ\sim △ABC$

$\therefore \frac{AP}{AB}=\frac{AQ}{AC}=\frac{PQ}{BC}$

$\Rightarrow \frac{3}{9}=\frac{5}{15}=\frac{PQ}{BC}$

$\therefore BC=3PQ$