- #1
autodidude
- 333
- 0
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)?
Thanks
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)?
Thanks