ClaribelG286733 ClaribelG286733

30-10-2022
Mathematics

Answered

In the diagram below, if the red lines are medians, and segment AE = 21, would be the length of the segment AO?

In the diagram below if the red lines are medians and segment AE 21 would be the length of the segment AO class=

Answer :

JaysaU250234 JaysaU250234

30-10-2022

We have a triangle with its medians AE, FB, and CD. The medians intersect at point O, which is called the centroid of the triangle.

The centroid is always 2/3 of the length of the median from each vertex.

Therefore if AE = 21, then AO must be 2/3 of that.

[tex]\begin{gathered} AO=\frac{2}{3}AE \\ \\ AO=\frac{2}{3}(21) \\ \\ AO=14 \end{gathered}[/tex]

The answer is option A, 14.

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