Problem
GEO-B1-M06-P011 Recover the Segment Ratio
#11
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), point \(D\) lies on \(BC\). It is known that \(S_{ABD}=24\), \(S_{ACD}=40\). Find \(BD:DC\).
These areas are in the ratio of bases \(BD\) and \(DC\).
Triangles \(ABD\) and \(ACD\) have the common height from \(A\). Therefore \(BD:DC=S_{ABD}:S_{ACD}=24:40=3:5\).
Converse use of an area ratio.