[latex]P_k - pole kwadratu[/latex] [latex]P_p - pole prostokata[/latex] [latex]a - dlugosc boku kwadratu[/latex] [latex]3a - dlugosc boku prostokata[/latex] [latex]a-5 - dlugosc boku prostokata[/latex] [latex]P_k = a^{2} [/latex] [latex]P_p = P_k + 8 cm^{2} [/latex] [latex]P_p = 3a*(a-5)[/latex] [latex]3a*(a-5) = a^{2}+8[/latex] [latex]3a^{2}-15a = a^{2} +8[/latex] [latex]3a^{2}-15a - a^{2}-8 = 0[/latex] [latex]2a^{2}-15a-8=0[/latex] [latex]Delta = 225+64 = 289[/latex] [latex]sqrt{Delta} = sqrt{289} = 17[/latex] [latex]a_1 = frac{15+17}{4} = frac{32}{4} = 8[/latex] [latex]a_2 = frac{15-17}{4} = frac{-2}{4} = -frac{1}{2}[/latex] [latex]Odrzucamy rozwiazanie a_2 = -frac{1}{2}, bo dlugosc nie moze byc[/latex] [latex]mniejsza od zera[/latex] [latex]a = 8[/latex] Spr. [latex]P_k = 8^{2} = 64 cm^{2}[/latex] [latex]P_p = 3*8 * (8 - 5) = 24*3 = 72 cm^{2} [/latex] [latex]P_p - P_k = 72 - 64 = 8 cm^{2}[/latex] [latex]Odp. Dlugosc boku kwadratu wynosi 8 cm.[/latex]
