Problem
GEO-B1-M06-P006 Ratio on a Side
#6
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), point \(D\) lies on \(BC\), and \(BD:DC=3:4\). Find \(S_{ABD}:S_{ABC}\).
Area \(ABD\) is the same fraction of the whole as \(BD\) is of \(BC\).
Since \(BD:DC=3:4\), we have \(BD:BC=3:7\). Triangles \(ABD\) and \(ABC\) have the common height from \(A\) to \(BC\). Therefore \(S_{ABD}:S_{ABC}=BD:BC=3:7\).
Useful for checking comparison of a part with the whole triangle.