1. Przekątna kwadratu
1)a)
[tex]17x^{2} + 17x^{2} = x^{2} \\289+289=x^{2} \\x^{2} = \sqrt{578} = \sqrt{289*2} = 17\sqrt{2}[/tex]
b)
[tex]x^{2} +x^{2} = 16^{2} \\2x^{2} = 256 /:2\\x^{2} = 128\\x = \sqrt{64*2} = 8\sqrt{2}\\[/tex]
2.
[tex]9^{2} +9^{2} =x^{2} \\ 162 = x^{2} \\ x^{2} = \sqrt{162} =\sqrt{81*2} = 9\sqrt{2}\\[/tex]
3.
[tex]x^{2} +x^{2} = 8^{2}\\ 2x^{2} = 64 /:2\\ x =\sqrt{32} = \sqrt{16*2} = 4\sqrt{2}[/tex]
2. Wysokość trójkąta równobocznego
a) [tex]h = \frac{a\sqrt{3} }{2} = \frac{12\sqrt{2} }{2} =6\sqrt{3}[/tex]
b) [tex]\frac{5\sqrt{3} }{2}[/tex]
