1.
[tex]e=\sqrt{45}\\S=6\sqrt{15}\\S=\cfrac{ef}{2}\\6\sqrt{15}=\cfrac{f\sqrt{45}}{2}\\12\sqrt{15}=f\sqrt{45}\\f=\cfrac{12\sqrt{15}}{\sqrt{45}}=12*\cfrac{\sqrt{15}}{\sqrt{45}}=12*\sqrt{\cfrac{15}{45}}=12*\sqrt{\cfrac{1}{3}}=12*\cfrac{1}{\sqrt{3}}=\cfrac{12}{\sqrt{3}}\\f=\cfrac{12}{\sqrt{3}}*\cfrac{\sqrt{3}}{\sqrt{3}}=\cfrac{12\sqrt{3}}{3}=4\sqrt{3}[/tex]
Odpowiedź A
2.
[tex]S_1=112cm^2\\S_2=1372cm^2\\S=a^2\\a_1=\sqrt{S_1}=\sqrt{112cm^2}=4\sqrt{7}cm\\a_2=\sqrt{S_2}=\sqrt{1372cm^2}=14\sqrt{7}cm\\n=\cfrac{a_2}{a_1}=\cfrac{14\sqrt{7}cm}{4\sqrt{7}cm}=\cfrac{14}{4}=\cfrac{7}{2}=3.5[/tex]
Bok mniejszego kwadratu jest 3.5 raza krótszy
3.
[tex]S=672cm^2\\S=6a^2\\a=\sqrt{\cfrac{S}{6}}\\V=a^3\\V=\left(\sqrt{\cfrac{S}{6}}\right)^3=\left(\sqrt{\cfrac{672cm^2}{6}}\right)^3=\left(\sqrt{112cm^2}\right)^3=\left(4\sqrt{7}cm\right)^3=448\sqrt{7}cm^3[/tex]
