Question

In the figure. $PQ\parallel BC$ and $AP:PB=$ $1:3$ Find $\frac{ar\left(\Delta APQ\right)}{ar\left(\Delta ABC\right)}$

• A. $1:4$
• B. $4:1$
• C. $1:9$
• D. $2:9$

Answer 1

The correct option is C $1:9$

Given $PQ\parallel BC⟹△ABC\sim △APQ$

$⟹\frac{AP}{AB}=\frac{AQ}{AC}=\frac{1}{3}$

$\frac{Ar\left(△APQ\right)}{Ar\left(△ABC\right)}=\frac{\frac{1}{2}\left(AP\right)\left(AQ\right)\sin A}{\frac{1}{2}\left(AB\right)\left(AC\right)\sin A}=\frac{1}{9}$