Calculate the Correct Length of the Tape – Mathematics Problem & Solution

Mathematics Problem – Example:

A line of true length 500 m, when measured by a 20 m tape, is reported to be 502 m long. The correct length of tape is?

Solution:

Given,

The line is measured long (502-500) = 2 m. Hence, the tape is short by some length and the actual length is not 20 m.

Hence,

True Length of Line = $\frac{{l}'}{l}\times$ measured length

Or, $500 = \frac{{l}'}{20}\times 502$

Or, $\frac{500\times 20}{502} = {l}'$

Or, ${l}' = 19.92 m$

Civil Engineering