2019 · Q27
Three parallel lines x, y and z are cut by two transversals m and n. Transversal m cuts the lines x, y, z at P, Q, R respectively; and transversal n cuts the lines x, y, z at L, M, N respectively. If PQ = 3 cm, QR = 9 cm and MN = 10.5 cm, then what is the length of LM?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A3 cm
- B3.5 cm
- C4 cm
- D4.5 cm
Explanation
Parallel lines cut by transversals give proportional intercepts (the intercept theorem): PQ/QR = LM/MN. Substituting, 3/9 = LM/10.5, so LM = 10.5/3 = 3.5 cm. The answer is (B).