A line AB between the stations A and B was measured as 348.28 m using a 20 m tape, too short by 0.05 m. What is the correct length of line AB?
- A349.15 m
- B348.41 m
- C347.41 mCorrect
- D346.15 m
Solution
Concept
A tape that is too short gives a measured length that is too long. So the true length is less than the measured length.
Formula
True length = (L' / L) × Measured length
Step-by-step solution
1. Nominal tape length L = 20 m. 2. Actual tape length L' = 20 - 0.05 = 19.95 m. 3. True length = (19.95 / 20) × 348.28 4. True length = 0.9975 × 348.28 = 347.41 m.
Explanation
The tape is shorter than 20 m, so it is laid out more times and the reading becomes too large. To correct this, we multiply the measured length by L'/L. The correct length is 347.41 m.
Why the other options are wrong
A (349.15) and B (348.41) are larger than the measured length, which is wrong for a short tape. D (346.15) has the wrong correction value.
Shortcut
Correction = 348.28 × 0.05/20 ≈ 0.87 m. Subtract it: 348.28 - 0.87 = 347.41 m.
Common mistake
Adding the correction instead of subtracting it for a too-short tape.
Correct answer: C) 347.41 m