Question

Determinati perimetrul unui romb stiind, ca are aria 32 $\sqrt{2}$ $cm^{2}$ si valoarea raportului diagonalelor $\sqrt{2}$ .

Answer 1

[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]