Question

find RN RP and SP

Answer 1

MNPQ is a parallelogram

Answer 2

MNPQ is a parallelogram, so MN = PQ, MQ = NP

PQ = QS + SP --> SP = PQ - QS = MN - QS = 5 - 3 = 2

NP = MQ = 2

Triangles MQS and RPS are similar triangles (because 3 corresponding angles are equal)

So we have \[\frac{RP}{MQ} = \frac{PS}{QS} = \frac{2}{3}\] ==> RP = 2*2/3 = 4/3

Conclusion: RP = 4/3, SP = 2, RN = RP + PN = 4/3 + 2 = 10/3