Question

In △ABC, ​ GF=17 in. ​ What is the length of CF¯¯¯¯¯? Enter your answer in the box. in. An acute triangle A B C is drawn. E is the midpoint of side A C. Segment A E and segment C E are labeled with double tick mark. F is the midpoint of side A B. Segment A F and segment F B are labeled with single tick mark. D is the midpoint of side B C. Segment B D and segment C D are labeled with triple tick mark. Line segment A D and C F and B F are medians of the triangle. Medians intersect with each other at an interior point labeled as G.

Answer 1

34 in.

Explanation:

It is a concept in trigonometry, that centroid of a triangle always divide median in the ratio of 2:1. Centroid is defined as a point at which the three medians of three sides of a triangle meet.

Since, it is a well known property of a centroid of a triangle. Now consider the median FGC as a line segment. the point G is distributing it in the ratio of

2:1

Now GC:GF = 2:1

Since, GF = 17 inches

GC = (17 x 2)

GC = 34 inches

Answer 2

51 cm

Explanation:

There is a well known property of medians of triangle

In any triangle, medians are concurrent and their common intersection point divides each median in proportion 2:1, counting the median parts from the vertex.

So, if G F = 17 cm, then AG = 34 cm, and the entire median C F = 17 +34 = 51 cm