In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.
ST = (5/7) .....SR = (5/7)QP → SR / QP = 5/7
Triangles SUT and QUP are similar
So VR = (5/7) QV → VR /QV = 5/7
So QV = (7/12)QR → QV / QR = 7/12
UV is parallel to SR
So
QV /QR =UV /SR
7 /12 = UV / 20
UV = (20)(7/12) = 140/12 = 35 / 3 = 11 + 2/3
