# Approximation and error

1. Feb 8, 2014

### chomool

Triangle ABC is an equilateral triangle with side 4 cm long which is measured corrected to the nearest cm.
Find the percentage error of the perimeter of triangle ABC.

3. The attempt at a solution
Is
[(0.5 x 2 x 3) / 12] x 100% correct?

the '2' here is the measurement errors of the starting pt and ending pt of line segment.

or

it should be:
[(0.5 x 3) / 12] x 100%

plz help~!

2. Feb 8, 2014

### Ray Vickson

There are two distinct possibilities:
(1) The triangle is known to be exactly equilateral, but having (three equal) sides measured with possible errors.
(2) The triangle was measured to have all three sides equal to 4 cm, but the individual sides may have (independent) measurement errors. Therefore, while the "measured" triangle is equilateral, the actual, true, triangle might not be.

I assume you want to go with interpretation (1), which is probably the one meant by the person who set the problem. In that case, it is straightforward: each side is between 3 cm and 5 cm, so the perimeter is between 9 cm and 15 cm, with 12 cm being the measured value. In other words, the perimeter is within the interval $12 \pm 3$ cm. The estimate of 12 cm could be "off" by as much as 3 cm.

3. Feb 8, 2014

### CompuChip

Doesn't "correct to the nearest cm" mean that it would be between 3.5 and 4.5? I.e. the value rounded to whole cm is 4.

4. Feb 8, 2014

### Ray Vickson

Yes, I think you are right.

5. Feb 8, 2014

### haruspex

The percentage error will also be a matter of ± so many %, so you don't need to double up here.