Problem
GEO-B1-M08-P003 A Small Triangle Inside a Large One
#3
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), points \(D\) and \(E\) lie on \(AB\) and \(AC\), and \(DE\parallel BC\). It is known that \(AD:DB=4:1\), \(BC=25\). Find \(DE\).
Triangles \(ADE\) and \(ABC\) are similar.
From \(DE\parallel BC\), \(\triangle ADE\sim\triangle ABC\). Since \(AD:AB=4:5\), we have \(DE:BC=4:5\). Therefore \(DE=25\cdot\frac{4}{5}=20\).
A standard mixed problem on recognising similarity.