Question 71147
Let L=length and h=height. In this case the equations for perimeter and area are:
2L+2h=32 and L*h=60
L=60/h
Now plug in L=60/h for L in the previous equation
{{{2(60/h)+2h=32}}}
{{{120/h+2h^2/h=32}}}Multiply 2nd term on left side to reach common denominator
{{{(120+2h^2)/h=32}}}Multiply both sides by h
{{{(120+2h^2)=32h}}}Get everything to one side by subtraction
{{{2h^2-32h+120=0}}}Now we have a quadratic to solve. Use the quadratic equation to solve.

*[invoke quadratic "h", 2, -32, 120 ] 
So the height is either 6 or 10. Lets solve for L.
{{{10L=60}}}
{{{L=60/10}}}
{{{L=6}}}If h=10 then L=6
{{{6L=60}}}
{{{L=60/6}}}
{{{L=6}}}If h=6 then L=10, see a pattern?