# Numerical Example For Error Due To Wrong Measuring Scale

Following numerical example shows that how to calculate correct length and area, if errors occur due to wrong measuring scale:

## Numerical Example

A surveyor measured the distance between two points marked on the plan drawn to a scale of 1cm = lm (R.F. = 1: 100) and found it to be 60m. Later he detected that he used a wrong scale of 1 cm = 50 cm (R.F. = 1: 50) for the measurement.

**(a)** Determine the correct length.

**(b)** What would be the correct area if the measured area is 70 m²?

## Mathematical Solution

a. Correct length = (R.F. of the wrong scale/R.F. of the correct scale) ⨯ measured length = [(1/50)/(1/100)] ⨯ 60 = 120m.

b. Correct area = (R.F. of the wrong scale/R.F. of the correct scale)² ⨯ measured area = [(1/50)/(1/100)]² ⨯ 70 = 280 m².

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