Question

A 50 m tape is held 2 m out of line, then its true length is:

• A. 49.96 m
• B. 48.96 m
• C. 49.02 m
• D. 48.02 m

Hint:

When measuring with tape held out of alignment, compute horizontal distance using: \[ \text{True length = \sqrt{(\text{Tape length)^2 - (\text{Offset)^2 \]

Answer 1

The Correct Option is A

Step 1: Visualizing the error.
When the tape is 2 m off from the straight line, it forms a right triangle:
Hypotenuse = tape = 50 m
One leg = lateral offset = 2 m Adjacent leg = true length (horizontal distance)
Step 2: Apply Pythagoras theorem: \[ \text{True length} = \sqrt{50^2 - 2^2} = \sqrt{2500 - 4} = \sqrt{2496} \approx 49.96 \text{ m} \]