Korzystamy ze wzoru na przekątną kwadratu
[tex]d=a\sqrt{2}\\\\\\a)\ \ 10\\\\d=a\sqrt{2}\\\\10=a\sqrt{2}\\\\a\sqrt{2}=10\ \ |:\sqrt{2}\\\\a=\frac{10}{\sqrt{2}}\\\\a=\frac{10}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{10\sqrt{2} }{\sqrt{2}\cdot\sqrt{2}}=\frac{\not10^5\sqrt{2}}{\not2_{1}}=5\sqrt{2}\\\\\\Obliczam\ \ obw\'od\ \ kwadratu\\\\Ob=4a\\\\Ob=4\cdot5\sqrt{2}=20\sqrt{2}[/tex]
[tex]b)\ \ 12\\\\d=a\sqrt{2}\\\\12=a\sqrt{2}\\\\a\sqrt{2}=12\ \ |:\sqrt{2}\\\\a=\frac{12}{\sqrt{2}}\\\\a=\frac{12}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{12\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}=\frac{\not12^6\sqrt{2}}{\not2_{1}}=6\sqrt{2}\\\\\\Obliczam\ \ obw\'od\ \ kwadratu\\\\Ob=4a\\\\Ob=4\cdot6\sqrt{2}=24\sqrt{2}[/tex]