Odpowiedź:
Wzór na przekątną kwadratu [tex]d=a\sqrt{2}[/tex]
[tex]a)\ \ 9\sqrt{2}cm\\\\d=a\sqrt{2}\\\\9\sqrt{2}=a\sqrt{2}\ \ /:\sqrt{2}\\\\9=a\\\\a=9cm\\\\Obliczamy\ \ obw\'od\ \ kwadratu\\\\Ob=4a\\\\Ob=4\cdot9cm=36cm\\\\Obliczamy\ \ pole\ \ kwadratu\\\\P=a^2\\\\P=9^2=81cm^2[/tex]
[tex]b)\ \ \frac{\sqrt{2}}{2}cm\\\\d=a\sqrt{2}\\\\\frac{\sqrt{2}}{2}=a\sqrt{2}\ \ /\cdot2\\\\\sqrt{2}=2\sqrt{2}a\ \ /:\sqrt{2}\\\\1=2a\\\\2a=1\ \ /:2\\\\a=\frac{1}{2}cm\\\\Obliczamy\ \ obw\'od\ \ kwadratu\\\\Ob=4a\\\\Ob=4\cdot\frac{1}{2}cm=2cm\\\\\\Obliczamy\ \ pole\ \ kwadratu\\\\P=a^2\\\\P=(\frac{1}{2})^2=\frac{1}{4}cm^2[/tex]
[tex]c)\ \ \frac{1}{2}cm\\\\d=a\sqrt{2}\\\\\frac{1}{2}=a\sqrt{2}\\\\\sqrt{2}a=\frac{1}{2}\ \ /:\sqrt{2}\\\\a=\frac{1}{2\sqrt{2}}=\frac{1}{2\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2\cdot2}=\frac{\sqrt{2}}{4}cm\\\\\\Obliczamy\ \ obw\'od\ \ kwadratu\\\\Ob=4a\\\\Ob=\not4\cdot\frac{\sqrt{2}}{\not4}cm=\sqrt{2}cm\\\\\\Obliczamy\ \ pole\ \ kwadratu\\\\P=a^2\\\\P=\frac{\sqrt{2}}{4}^2=\frac{(\sqrt{2})^2}{4^2}=\frac{2}{16}= \frac{1}{8}cm^2[/tex]
[tex]d)\ \ 3x\\\\d=a\sqrt{2}\\\\3x=a\sqrt{2}\\\\\sqrt{2}a=3x\ \ /:\sqrt{2}\\\\a=\frac{3x}{\sqrt{2}}\\\\a=\frac{3x}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{3x\sqrt{2}}{2}=\frac{3\sqrt{2}x }{2}cm\\\\\\Obliczamy\ \ obw\'od\ \ kwadratu\\\\Ob=4a\\\\Ob=\not4^2\cdot\frac{3\sqrt{2}x}{\not2_{1}}=2\cdot3\sqrt{2}x=6\sqrt{2}x\ \ cm\\\\\\Obliczamy\ \ pole\ \ kwadratu\\\\P=a^2\\\\P=(\frac{3\sqrt{2}x}{2})^2=\frac{3^2\cdot(\sqrt{2}x)^2}{2^2}=\frac{9\cdot2x^2}{4}=\frac{18x^2}{4}=\frac{9x^2}{2}cm^2[/tex]
