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Approximation and error

  1. Feb 8, 2014 #1
    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
    [(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.


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

    plz help~!
  2. jcsd
  3. Feb 8, 2014 #2

    Ray Vickson

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    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.
  4. Feb 8, 2014 #3


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    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.
  5. Feb 8, 2014 #4

    Ray Vickson

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    Yes, I think you are right.
  6. Feb 8, 2014 #5


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