Percentage Error of Equilateral Triangle Perimeter

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Homework Help Overview

The problem involves calculating the percentage error of the perimeter of an equilateral triangle with sides measured to the nearest centimeter. The triangle has a side length of 4 cm, and participants are discussing the implications of measurement errors on the perimeter calculation.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are examining different interpretations of the measurement error, questioning whether the triangle's sides are known to be exactly equal or if they could have independent measurement errors. There is also discussion on the correct formula for calculating percentage error, with some participants suggesting different approaches to the calculation.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem and questioning the assumptions behind the measurement error. Some guidance has been offered regarding the implications of rounding and the nature of the measurement errors, but no consensus has been reached.

Contextual Notes

Participants are considering the implications of the phrase "correct to the nearest cm" and how it affects the range of possible values for the side lengths of the triangle. There is also mention of potential confusion regarding the calculation of percentage error based on different interpretations of the problem setup.

chomool
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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.

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%

please help~!
 
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chomool said:
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.


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%

please help~!

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.
 
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.
 
CompuChip said:
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.

Yes, I think you are right.
 
chomool said:
the '2' here is the measurement errors of the starting pt and ending pt of line segment.
The percentage error will also be a matter of ± so many %, so you don't need to double up here.
 

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