Problem
GEO-B1-M06-P014 A Parallel Side Inside a Triangle
#14
★★★☆☆ Level 3 of 5
In triangle \(ABC\), points \(D\in AB\), \(E\in AC\), and \(DE\parallel BC\). It is known that \(AD:DB=2:3\). Find \(S_{ADE}:S_{ABC}\).
Triangles \(ADE\) and \(ABC\) are similar; areas are in the square of the ratio.
Since \(DE\parallel BC\), \(\triangle ADE\sim\triangle ABC\). We have \(AD:AB=2:5\). Therefore the area ratio equals the square of the side ratio: \(S_{ADE}:S_{ABC}=4:25\).
Important not to confuse the length ratio \(2:5\) with the area ratio \(4:25\).