Odpowiedź:
a)
[tex]|AE| = \frac{6\sqrt{3} }{2} = 3\sqrt{3}\\|AS| = \frac{2}{3} |AE|} = \frac{2}{3} * 3\sqrt{3} = 2\sqrt{3}\\x^{2} +(2\sqrt{3} )^{2} = 10^{2}\\x^{2} + 12 = 100\\x^{2} = 88\\x = \sqrt{88} = \sqrt{4*22} = \sqrt{4} * \sqrt{22} = 2\sqrt{22}\\Odp. x = 2\sqrt{22}[/tex]
b)
[tex]|AE| = \frac{2\sqrt{3} * \sqrt{3} }{2} = 3\\|AS| = \frac{2}{3}|AE| = \frac{2}{3} * 3 = 2\\y^{2} = 10^{2} + 2^{2}\\y^{2} = 100 + 4\\y = \sqrt{204} = \sqrt{4 * 26} = \sqrt{4} * \sqrt{26} = 2\sqrt{26}\\Odp. y = 2\sqrt{26}[/tex]
c)
[tex]|AE| = \frac{6\sqrt{3} }{2} = 3\sqrt{3} \\|SE| = \frac{1}{3}|AE| = \frac{1}{3} * 3\sqrt{3} = \sqrt{3} \\ z^{2} = 7^{2} + (\sqrt{3} )^{2}\\z^{2} = 49 + 3\\z^{2} = 52\\z = \sqrt{52} = \sqrt{4 * 13} = \sqrt{4} * \sqrt{13} = 2\sqrt{13}\\Odp. z = 2\sqrt{13}[/tex]
