1. Limited time only! Sign up for a free 30min personal 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!

Formula for lengths of a rectangle - why does it give both lengths?

  1. Jun 19, 2012 #1
    Why does the formula [P±√(P^2-16A)]/4 give the values of either of two different lengths of a rectangle? (P is perimeter and A is area)

    I derived it by solving two simultaneous equations, A = xy and P=x+y and then applying the quadratic formula to the resulting second-order equation 2y^2 + Py+2A thus getting y=[P±√(P^2-16A)]/4

    I tried out some numbers just to test it out and was surprised that both solutions were lengths of the rectangle, so it gave y but also x…I fail to see how this so, shouldn't it only give the length y (or x, if I'd eliminated y instead when I solved the simultaneous equations)?

  2. jcsd
  3. Jun 20, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The equations cannot 'know' which is x and which is y. If x = A, y = B is a solution then so is x = B, y = A.
    Btw, the perimeter would be 2x+2y.
  4. Jun 20, 2012 #3
    I believe its a typo, his derivation is correct in the quadratic formula, the quadratic had a sign error also
  5. Jun 20, 2012 #4
    Hmmm...I guess that makes sense...I'll think about it, thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook