1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    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. jcsd
  3. Feb 8, 2014 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    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

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

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

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The percentage error will also be a matter of ± so many %, so you don't need to double up here.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Approximation and error
  1. Approximating Angles (Replies: 4)

  2. Linear approximations (Replies: 1)

Loading...