Question

If X is the centroid of △ABC, GE=12, BF=57, GC=18, and BC=32. Find GD.

A) 8
B) 9
C) 10
D) 11

Answer 1

To find GD, we can subtract the lengths of GE and BF from BC, and divide the result by 2.

Step-by-step explanation:

To find GD, we need to first find the length of GD in terms of GC. The centroid divides each median into two parts, with the longer part being twice as long as the shorter part. So, GD is twice as long as GC. Since GC = 18, GD = 2 * 18 = 36. However, we are given the lengths of GE and BF. To find GD, we can subtract the lengths of GE and BF from BC, and divide the result by 2. GD = (BC - GE - BF) / 2 = (32 - 12 - 57) / 2 = -37 / 2 = -18.5.

However, lengths cannot be negative, so we discard the negative value. Therefore, GD = 18.5.