$x=\frac{5}{12}$  $S=xy=60$  $y\times \frac{5}{12}y=60\Rightarrow {{y}^{2}}=\frac{12\times 60}{5}=144\Rightarrow y=12$  ${{x}^{2}}={{12}^{2}}+{{5}^{2}}\Rightarrow {{x}^{2}}=144+25\Rightarrow x=13$  $x=\frac{5}{12}\,\,\,\,\,\,\,\,x\times y=60\Rightarrow \frac{5}{12}y\times y=60$  ${{y}^{2}}={{12}^{2}}\Rightarrow y=12\,\,\,,\,\,\,x=5$  ${{12}^{2}}+{{5}^{2}}={{z}^{2}}\Rightarrow 144+25=169\Rightarrow z=13$