Zadanie 7.
Aby rozwiązać zadanie, korzystam ze wzoru na długość przekątnej sześcianu
[tex]d = a\sqrt{3}[/tex]
a) d = 3 cm
[tex]d = a\sqrt{3} \\\\ 3 = a\sqrt{3} ~| :\sqrt{3} \\\\ \frac{3}{\sqrt{3} } = \frac{a\sqrt{3} }{\sqrt{3} } \\\\ a = \frac{3}{\sqrt{3} }~| \cdot \sqrt{3} \\\\ a = \frac{3\sqrt{3} }{\sqrt{3} \cdot \sqrt{3} } \\\\ a = \frac{3\sqrt{3} }{3} \\\\ a = \sqrt{3}~cm[/tex]
b) d = 33 cm
[tex]d = a\sqrt{3} \\\\ 33 = a\sqrt{3}~| :\sqrt{3} \\\\ \frac{33}{\sqrt{3} } =\frac{a\sqrt{3} }{\sqrt{3} } \\\\ a = \frac{33}{\sqrt{3} }~| \cdot \sqrt{3} \\\\ a = \frac{33 \sqrt{3} }{\sqrt{3} \cdot \sqrt{3} } \\\\ a = \frac{33\sqrt{3} }{3} \\\\ a = 11\sqrt{3}~cm[/tex]
c) d = 306
[tex]d = a\sqrt{3} \\\\ 306 = a\sqrt{3}~| :\sqrt{3} \\\\ \frac{306}{\sqrt{3} } =\frac{a\sqrt{3} }{\sqrt{3} } \\\\ a = \frac{306}{\sqrt{3} }~| \cdot \sqrt{3} \\\\ a = \frac{306 \sqrt{3} }{\sqrt{3} \cdot \sqrt{3} } \\\\ a = \frac{306\sqrt{3} }{3} \\\\ a = 102\sqrt{3}~cm[/tex]
d) d = 60 cm
[tex]d = a\sqrt{3} \\\\ 60 = a\sqrt{3}~| :\sqrt{3} \\\\ \frac{60}{\sqrt{3} } = \frac{a\sqrt{3} }{\sqrt{3} } \\\\ a = \frac{60}{\sqrt{3} }~| \cdot \sqrt{3} \\\\ a = \frac{60 \sqrt{3} }{\sqrt{3} \cdot \sqrt{3} } \\\\ a = \frac{60\sqrt{3} }{3} \\\\ a = 20\sqrt{3}~cm[/tex]
