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If d is the centroid of triangle pqr, pa = 17, db = 9, and dq = 14, find each missing measure?

User Minjae
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Final answer:

Using the property of centroids being the point where medians intersect, the lengths of the medians from vertices P, Q, and R are calculated based on the given segments PD, DQ, and DB.

Step-by-step explanation:

The problem described involves finding the missing measures in a triangle where d is the centroid. The centroid of a triangle divides the medians into segments with a 2:1 ratio, where the portion closer to the vertex is twice as long as the segment closer to the midpoint of the triangle's side. Given pa = 17, db = 9, and dq = 14, we can determine the lengths of the remaining segments.

Since PA is the full length of the median from P to side QR, and PD is two-thirds of that (since D is the centroid), we can express PD as (2/3)PA. Therefore, AD (the third segment of the median from P to QR) would be (1/3)PA. Using PA = 17, PD would be (2/3) * 17 = 34/3, and AD would be 17/3.

For DQ and DB, the same logic applies. The full length of the medians QB and QD would be three times the given lengths DB and DQ. Therefore, QB = 3 * 9 = 27 and QD = 3 * 14 = 42.

User Rafael De Castro
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