Question

P is the centroid of triangle ABC. AE=21,CD=14, and BF=11 What is the length of AP

Answer 1

The length of AP is 14 units

Step-by-step explanation:

The centroid point of a triangle is:

• The point of intersection of the three medians of the triangle
• The centroid point divides each median into two segments at a ratio 2 : 1 from its vertex
• The length of the segment from the vertex to the centroid is $\frac{2}{3}$ of the length of the median
• The length of the segment from the centroid to the base is $\frac{1}{3}$ of the length of the median

Look to the attached figure

In Δ ABC

∵ D is the mid-point of AB

∵ E is the mid-point of BC

∵ F is the mid-point of AC

∵ AE , BF and CD are the medians of the triangle

∵ AE , BF and CD are intersected at P

∴ P is the centroid of the triangle

- By using the rule above

∴ AP = $\frac{2}{3}$ AE

∵ AE = 21 units

∴ AP = $\frac{2}{3}$ × 21

∴ AP = 14 units

The length of AP is 14 units

Learn more:

You can learn more about the triangles in brainly.com/question/3358617

#LearnwithBrainly