Question

In $△PQR$, $LM\parallel QR$ and $PM:MR=3:4$. Calculate$\frac{PL}{PQ}$ and then $\frac{LM}{QR}$

• A. $\frac{PL}{PQ}=\frac{LM}{QR}=\frac{3}{7}$
• B. $\frac{PL}{PQ}=\frac{LM}{QR}=\frac{5}{7}$
• C. $\frac{PL}{PQ}=\frac{LM}{QR}=\frac{9}{7}$
• D. $\frac{PL}{PQ}=\frac{LM}{QR}=\frac{1}{7}$

Answer 1

Answer: (A)

$\frac{PL}{PQ}=\frac{LM}{QR}=\frac{3}{7}$

Given, $LM\parallel QR$, $PM:MR=3:4$
$\frac{PM}{MR}=\frac{3}{4}$
$\frac{PM+MR}{MR}=\frac{3+4}{4}$
$\frac{PR}{MR}=\frac{7}{4}$
Now, In $△PLM$ and $△PQR$
$\angle LPM=\angle QPR$ (Common angle)
$\angle PLM=\angle PQR$ (Corresponding angles)
$\angle PML=\angle PRQ$ (Corresponding angles)
Thus, $△PLM\sim △PQR$ (AAA rule)
Hence, $\frac{PL}{PQ}=\frac{LM}{QR}=\frac{PM}{PR}$ (Corresponding sides)
$\frac{PL}{PQ}=\frac{LM}{QR}=\frac{3}{7}$