Problem
GEO-B1-M08-P015 A Point on a Cevian
#15
★★★★☆ Level 4 of 5
The area of triangle \(ABC\) is \(120\). Point \(D\) lies on \(BC\), and point \(E\) lies on \(AD\), with \(AE:ED=3:2\). Find \(S_{BCE}\).
Compare the heights of points \(E\) and \(A\) to base \(BC\).
Triangles \(BCE\) and \(BCA\) have common base \(BC\). Since \(D\) lies on \(BC\), the height of point \(E\) to \(BC\) is \(ED:AD=2:5\) of the height of point \(A\). Therefore \(S_{BCE}=\frac{2}{5}\cdot120=48\).
The problem looks like segments, but the natural method is areas.