Answers:
AQ = 8
QD = 4
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Explanation:
A median goes from a vertex to the midpoint of the opposite side. The medians of this triangle are segments AD, BE, and CF.
The three medians intersect at the centroid. The centroid cuts the median AD such that
- AQ is 2/3 as long as AD
- QD is 1/3 as long as AD
Note how 2/3+1/3 = 3/3 = 1
Since AD = 12, we know that
- AQ = (2/3)*AD = (2/3)*12 = 8
- QD = (1/3)*AD = (1/3)*12 = 4
As a check,
AQ+QD = 8+4 = 12 = AD
So AQ+QD = AD is a true equation.
