Problem
GEO-B1-M03-P005 A Small Triangle Inside a Large One
#5
★☆☆☆☆ Level 1 of 5
In triangle \(ABC\), points \(D\in AB\), \(E\in AC\), and \(DE\parallel BC\). It is known that \(AD:AB=3:5\), \(BC=25\). Find \(DE\).
Triangles \(ADE\) and \(ABC\) are similar.
Since \(DE\parallel BC\), \(\triangle ADE\sim\triangle ABC\). Hence \(\frac{DE}{BC}=\frac{AD}{AB}=\frac{3}{5}\). Therefore \(DE=25\cdot\frac{3}{5}=15\).
The basic template for all problems with a parallel side inside a triangle.