Odpowiedź:
a)
[tex]d=a\sqrt{2}[/tex]
[tex]9\sqrt{2}=a\sqrt{2}[/tex]
[tex]a=9[/tex]
[tex]Obw=4a[/tex]
[tex]Obw=4*9=36[/tex]
[tex]P=a^2[/tex]
[tex]P=9*9[/tex]
[tex]P=81cm^2[/tex]
b)
[tex]d=a\sqrt{2}[/tex]
[tex]\frac{\sqrt{2} }{2} =a\sqrt{2}[/tex] /:[tex]\sqrt{2}[/tex]
[tex]a=\frac{1}{2}[/tex]
[tex]Obw=4a=4*\frac{1}{2} =2cm[/tex]
[tex]P=\frac{1}{2} *\frac{1}{2} =\frac{1}{4} cm^2[/tex]
c)
[tex]d=a\sqrt{2}[/tex]
[tex]\frac{1}{2} =a\sqrt{2}[/tex] /:[tex]\sqrt{2}[/tex]
[tex]a=\frac{1}{2\sqrt{2} }[/tex]
[tex]a=\frac{\sqrt{2} }{4}[/tex]
[tex]Obw=4a=4*\frac{\sqrt{2} }{4} =\sqrt{2}cm[/tex]
[tex]P=(\frac{\sqrt{2}} {4} )^2=\frac{2}{16} =\frac{1}{8} cm^2[/tex]
d)
[tex]d=a\sqrt{2}[/tex]
[tex]3x=a\sqrt{2}[/tex] /:[tex]\sqrt{2}[/tex]
[tex]a=\frac{3x}{\sqrt{2} }[/tex]
[tex]a=\frac{3x\sqrt{2} }{2}[/tex]
[tex]Obw=4a=4*\frac{3x\sqrt{2} }{2} =2*3x\sqrt{2} =6x\sqrt{2} cm[/tex]
[tex]P=(\frac{3x\sqrt{2} }{2})^2= \frac{9*2x^2}{4} =\frac{9x^2}{2} cm^2[/tex]
