Select The Correct Answer From Each Drop-down Menu - Gauthmath

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Question

In △ ABC , G is the intersection of the three medians. If GF=18 , find BF. Answer Attempt 1 out of 2SHOW LESS129

Solution

user avatar imageAnswer\(54\)ExplanationStep 1: Recognize that the intersection of the medians of a triangle (known as the centroid) divides each median into two segments, with the segment from the vertex to the centroid being twice as long as the segment from the centroid to the midpoint of the opposite side. Step 2: Apply the property that the segment from the centroid to a vertex is \(\frac{1}{3}\) the length of the median from that vertex to the midpoint of the opposite side. Step 3: Since \(GF = 18\), we can find \(BF\) by multiplying \(GF\) by 3, because \(BF = 3 \times GF\). Step 4: Calculate \(BF\) as \(BF = 3 \times 18 = 54\). Therefore, \(BF\) is \(54\).Click to rate:92.8(514 votes)Search questionBy textBy image/screenshotDrop your file here orClick Hereto upload

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