A line AB between the stations A and B was measured as 348 m using a 20 m tape, too short by 0·05 m. What is the correct length of AB ?
- A347·41 m
- B349·15 m
- C347·13 mCorrect
- D348·87 m
Solution
Concept
Correction for a short tape
Formula
True length = measured length × (actual tape length / nominal length)
Step-by-step solution
1. Actual tape length = 20 − 0.05 = 19.95 m. 2. True length = 348 × 19.95 / 20 = 347.13 m.
Explanation
A tape that is too short records more length than the true distance, so the correction is negative and the true length is smaller than the measured one.
Why the other options are wrong
349.15 m and 348.87 m are larger than the measured value (wrong sign for a short tape). 347.41 m is not equal to 348 × 19.95/20.
Shortcut
Tape short → measured length is too big → reduce it.
Common mistake
Adding the correction (as for a long tape).
Correct answer: C) 347·13 m