2021 · Q12
ABC is a triangle right angled at B. Let M and N be two points on AB such that AM = MN = NB. Let P and Q be two points on AC such that PM is parallel to QN and QN is parallel to CB. If BC = 12 cm, then what is (PM + QN) equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A10 cm
- B11 cm
- C12 cm
- D13 cm
Explanation
AM = MN = NB places M and N at 1/3 and 2/3 of AB from A. Since PM ∥ QN ∥ CB, triangles APM and AQN are similar to ABC with linear ratios 1/3 and 2/3. Thus PM = 12/3 = 4 cm and QN = 2·12/3 = 8 cm, so PM + QN = 12 cm. Hence option C.