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Answer :
Final answer:
To find lengths PN and QP, we use the fact that the centroid divides the median in a 2:1 ratio. Since QN equals 33, PN is 22 and QP is 11.
Explanation:
The student is asking how to find the lengths of PN and QP given that QN equals 33 and point P is the centroid of triangle LMN. In a triangle, the centroid divides the median in a 2:1 ratio, meaning that the portion of the median from the vertex to the centroid is twice as long as the portion from the centroid to the midpoint of the opposite side.
Since QN is the median of triangle LMN from vertex Q to midpoint N, and P is the centroid, we can say that:
- PN = (2/3) * QN
- QP = (1/3) * QN
Substituting the given length for QN, we get:
- PN = (2/3) * 33
- QP = (1/3) * 33
Calculating these, we find:
- PN = 22
- QP = 11
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