2025 · Q38
A man starting from a place P went x metre (x > 120 m) East before turning South. He went 40 m straight before turning to West. He went 60 m to reach a place Q. From Q he went 200 m North and reached a place R. If PR = 200 m, then what is x equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A150 m
- B180 m
- C200 m
- D240 m
Explanation
Place P at (0,0): after going x east, 40 south and 60 west, Q = (x−60, −40); going 200 north gives R = (x−60, 160). PR = 200 gives (x−60)² + 160² = 200², so (x−60)² = 14400 and x − 60 = 120 (x > 120), giving x = 180 m, option (b).