Problem
GEO-B2-M07-P020 Square of a Ratio
#20
★★★★☆ Level 4 of 5
In triangle \(ABC\), point \(P\in AC\), and line \(PQ\parallel BC\) is drawn through \(P\), with \(Q\in AB\). If \([APQ]:[ABC]=9:25\), find \(AP:PC\).
The ratio of areas of similar triangles is the square of the ratio of sides.
From similarity \(APQ\sim ABC\), \(\left(\frac{AP}{AC}\right)^2=\frac{9}{25}\), hence \(\frac{AP}{AC}=\frac{3}{5}\). Then \(PC=\frac{2}{5}AC\), so \(AP:PC=3:2\).
Useful for problems with parallel sections.