In triangle ABC, P and Q are the mid points of AB and AC, respectively. R is a point on PQ such that PR : RQ = 3 : 5 and QR = 20 cm, then what is the length (in cm) of BC?

66.66 24 64 40

64

Let the length of PQ be x PR : RQ = 3 : 5 x ×  \(\frac{5}{8}\) = 20 = x = 20 × \(\frac{8}{5}\) = 32 cm. PQ = 32 cm PQ = \(\frac{1}{2}\)BC = BC = 2 x PQ = BC = 2 x 32 = 64 cm. Therefore, length of BC is 64 cm.