[tex]\dfrac{d_1\cdot d_2}{2}=32\sqrt{2}\Rightarrow d_1 \cdot d_2 =64\sqrt{2}\Rightarrow d_1=\dfrac{64\sqrt{2}}{d_2}\\
\dfrac{d_1}{d_2}=\sqrt{2} \Leftrightarrow \dfrac{64\sqrt{2}}{d_2} \cdot \dfrac{1}{d_2}=\sqrt{2} \\
\dfrac{64\sqrt{2}}{d_{2}^{2}}=\sqrt{2} \Rightarrow d_2=8 \Rightarrow d_1=8\sqrt{2}\\
l=\sqrt{d_{2}^{2}+d_{1}^{2}}=\sqrt{192}=8\sqrt{3} \Rightarrow P_{romb}=32\sqrt{3}\; cm[/tex]
