L = lenght
W = width
[tex]L * W = 60 \\
2L + 2W=32\\\\
L = \frac{32-2W}{2}\\
\frac{32-2W}{2}*W = 60\\
(16-W)*W = 60\\
-W^{2} + 16W -60 = 0\\\\
d = 16^{2} - 4*1*60 = 256 - 240 = 16 \\\\
W1 = \frac{-16+\sqrt{16}}{-2} = \frac{-12}{-2} = 6\\
W2 = \frac{-16-\sqrt{16}}{-2} = \frac{-20}{-2} = 10\\
L1 = 10\\
L2 = 6\\
[/tex]
so
{L,W} = {6,10} or {10,6}
but L > W so
L = 10
W = 6
