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Answer :
Final answer:
By utilizing the properties of a centroid in a triangle, which divides medians in a 2:1 ratio, we find that PN = 7 and QP = 14, given QN = 21.
Explanation:
By the properties of a centroid in a triangle, we know that the centroid divides the medians in a 2:1 ratio, counting from the vertex to the midpoint of the opposite side. Since QN is the entire length of the median from Q to N, and knowing the 2:1 division property, we can find both PN and QP.
To find PN, we recognize that PN is 1/3 of QN because PN is the shorter segment from the centroid to the midpoint of the side. Therefore, PN = QN / 3 = 21 / 3 = 7.
To find QP, we can deduce it is 2/3 of QN, since QP is the longer segment from the vertex to the centroid. Consequently, QP = 2/3 * QN = 2/3 * 21 = 14.
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