Question

1. point l is a centroid of the triangle fwd. if rl = 54 cm, what is rd? 100 cm 81 cm 162 cm 58 cm

Explanation:

Step1: Recall centroid property

In a triangle, the centroid divides each median into a ratio of \(2:1\) (from vertex to centroid : centroid to midpoint). Also, the segment from the vertex to the midpoint (median) and the segment from the midpoint to the other side (here, \(RL\) and \(RD\) – wait, actually, looking at the diagram, \(R\) is the midpoint of \(WF\) (since there are markings), and \(L\) is the centroid. So the line \(RD\) – wait, no, the median from \(D\) to \(WF\) would have midpoint \(R\), and centroid \(L\) divides \(DR\) (wait, maybe I got the segments wrong). Wait, actually, in a triangle, the centroid is the intersection of medians. A median connects a vertex to the midpoint of the opposite side. So if \(R\) is the midpoint of \(WF\) (since \(WR = RF\) as per the markings), then \(DR\) is a median? Wait, no, the median from \(D\) would go to midpoint of \(WF\), which is \(R\), so \(DR\) is a median. Then the centroid \(L\) divides the median \(DR\) into \(DL:LR = 2:1\)? Wait, no, the centroid divides the median into a ratio of \(2:1\) where the longer segment is from the vertex to the centroid. Wait, maybe I mixed up. Let's correct: The centroid \(L\) is on the median, and the distance from the vertex to centroid is twice the distance from centroid to midpoint. So if \(RL\) is the segment from midpoint \(R\) to centroid \(L\), then \(DL = 2 \times RL\), and \(RD = RL + DL = RL + 2RL = 3RL\). Wait, let's check: If \(R\) is the midpoint of \(WF\), then \(DR\) is the median. The centroid \(L\) lies on \(DR\), and \(RL\) is the part from midpoint \(R\) to centroid \(L\), so the length from \(D\) to \(L\) is twice \(L\) to \(R\). So \(DL = 2 \times RL\), so \(RD = RL + DL = RL + 2RL = 3RL\).

Step2: Calculate RD

Given \(RL = 54\) cm, then \(RD = 3 \times 54\) cm.
\(3 \times 54 = 162\) cm.

Answer:

162 cm (corresponding to the option with 162 cm)