Answer:
The length of AP will be 14 units.
Step-by-step explanation:
As P is the centroid of ΔABC as shown in question figure.
As the side AB of the triangle has the midpoint D, the side AC of the triangle has the midpoint F and the side BC of the triangle has the
midpoint E.
Hence, CD, BF and AE being medians of ΔABC.
The point of intersection of these medians will be the centroid of the triangle. Hence, P is the centroid of ΔABC
According to rule, the centroid point of the triangle ΔABC divides each median into two segments in the ratio 2 : 1.
So,
[tex]AP = \frac{2}{3} AE[/tex]
As the value of AE = 21
So,
[tex]AP = \frac{2}{3} (21)[/tex]
AP = 14
So, the length of AP will be 14 units.
Keywords: centroid, triangle
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