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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. The correct length of AB is:

  • A.370.2 m
  • B.374.2 m
  • C.340.1 m
  • D.347.4 m

Answer: D

The correct length of AB is 347.4 m.

A tape that is too short reads more than the true distance, because each 'tape length' laid down actually covers only 19.95 m:

\[ \begin{aligned} L &= \frac{L'}{L_n} \times l' = 348.28 \times \frac{19.95}{20} \\ &= 347.41\ \text{m} \end{aligned} \]

So the true length is a little less than the measured one. The other options are far from 348.28 m, while a 0.05 m error per 20 m can change the length by less than 1 m, so none of them can be right.

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