[tex]zad.1\\\\P\Delta=\dfrac{a^{2} \sqrt{3} }{4} ~~wzor~~na ~~pole ~~trojkata~~~rownobocznego\\\\P\Delta=\dfrac{a^{2} \sqrt{3} }{4} ~~\land ~~P\Delta=8\sqrt{3} \\\\\dfrac{a^{2} \sqrt{3} }{4} =8\sqrt{3}~~~~\vert \cdot 4\\\\a^{2} \sqrt{3}=32\sqrt{3} ~~~~\vert \div \sqrt{3} \\\\a^{2} =32~~\land ~~a>0~~\Rightarrow~~ a =\sqrt{32} \\\\a=4\sqrt{2} ~~tyle ~~wynosi~~dlugosc~~boku~~trojkata~~rownobocznego\\\\h=\dfrac{a\sqrt{3} }{2} ~~wysokosc~~w ~~trojkacie~~rownobocznym\\\\[/tex]
[tex]h=\dfrac{a\sqrt{3} }{2}~~\land ~~a=4\sqrt{2} ~~\Rightarrow~~h=\dfrac{4\sqrt{2} \cdot \sqrt{3} }{2} \\\\h=2\sqrt{6} ~~tyle ~~wynosi~~wysokosc~~w ~~trojkacie~~rownobocznym\\\\Odp. F\\\\\\\\zad.2\\\\P\Box =a^{2} ~~wzor~~ na ~~pole ~~kwadratu\\\\P\Box =a^{2}~~\land ~~ P=20~cm^{2} ~~\Rightarrow ~~a^{2} =20~cm^{2} \\\\a^{2} =20~cm^{2} ~~\land ~~a>0\\a=\sqrt{20} ~cm\\\\a=2\sqrt{5} ~cm~~tyle ~~wynosi~~dlugosc~~boku~~kwadratu\\\\d=a\sqrt{2} ~~dlugosc~~przekatnej~~kwadratu \\\\[/tex]
[tex]d=a\sqrt{2}~~\land~~a=2\sqrt{5} ~cm~~\Rightarrow ~~d=2\sqrt{5}\cdot \sqrt{2}~cm\\\\d=2\sqrt{10} ~cm=2\sqrt{5} \cdot \sqrt{2} ~cm ~~tyle ~~wynosi~~dlugosc~~przekatnej~~kwadratu\\\\a=2\sqrt{5}~cm ~~oraz ~~d=2\sqrt{5} \cdot \sqrt{2} ~cm~~\Rightarrow[/tex]
[tex]~~przekatna~~kwadratu~~jest~~dluzsza~~od~~boku~~kwadratu~~o~~\sqrt{2} \\\\Odp. F[/tex]
