Question

answer attempt 1 out of 3
in triangle abc, e is the point of concurrency of the called
the .
if ae = 21, then ed = and ad = .

Explanation:

Step1: Identify the point E

In triangle \(ABC\), \(E\) is the centroid (point of concurrency of medians). A median connects a vertex to the midpoint of the opposite side, and the centroid divides each median in a ratio of \(2:1\) (with the longer segment being from the vertex to the centroid).

Step2: Find ED

Given \(AE = 21\), and the ratio \(AE:ED=2:1\). Let \(ED = x\), then \(\frac{AE}{ED}=\frac{2}{1}\), so \(\frac{21}{x}=\frac{2}{1}\). Cross - multiplying gives \(2x = 21\), so \(x=\frac{21}{2}=10.5\). Thus, \(ED = 10.5\).

Step3: Find AD

Since \(AD=AE + ED\), and \(AE = 21\), \(ED = 10.5\), then \(AD=21 + 10.5=31.5\).

Answer:

ED = 10.5, AD = 31.5