In triangle ABC the three medians meet at G, and D is the midpoint of BC. If GD = 4 cm and the median drawn from B measures 15 cm, what is AG + BG?

The centroid cuts every median in the ratio 2 : 1 measured from the vertex. On median AD the short piece is GD = 4 cm, so AG = $2\times 4=8$ cm. On the median from B the whole length is 15 cm, so BG = ⅔ × 15 = 10 cm. Hence AG + BG = 18 cm. Using ⅓ instead of ⅔ for BG gives the trap 13 cm, and taking the full 15 cm as BG gives 23 cm.