a)
a = 4
h = ?
[tex]a^{2}[/tex]+ [tex]b^{2}[/tex] = [tex]c^{2}[/tex] / [tex]2^{2}[/tex] + [tex]h^{2}[/tex] = [tex]8^{2}[/tex] / 4 + [tex]h^{2}[/tex] = 64
[tex]h^{2}[/tex] = 60
h = [tex]\sqrt{60}[/tex] = [tex]\sqrt{4*15}[/tex] = [tex]2\sqrt{15}[/tex]
Pp = a * a = 4 * 4 = 16
Pb = [tex]\frac{a * h}{2}[/tex] = [tex]\frac{ 4 * 2\sqrt{15} }{2}[/tex] = [tex]4\sqrt{15}[/tex]
Pc = 16 + 4 * [tex]4\sqrt{15}[/tex] = 16 + [tex]16\sqrt{15}[/tex]
b)
a = 4
x = ?
[tex]a^{2}[/tex]+ [tex]b^{2}[/tex] = [tex]c^{2}[/tex] / [tex]2^{2}[/tex] + [tex]x^{2}[/tex] = [tex]4^{2}[/tex] / 4 + [tex]x^{2}[/tex] = 16
[tex]x^{2}[/tex] = 12
x = [tex]\sqrt{12}[/tex] = [tex]\sqrt{ 4 * 3}[/tex] = [tex]2\sqrt{3}[/tex]
Pp = [tex]\frac{a * h}{2}[/tex] = [tex]\frac{ 4 * 2\sqrt{3} }{2}[/tex] = [tex]4\sqrt{3}[/tex]
h = ?
[tex]a^{2}[/tex]+ [tex]b^{2}[/tex] = [tex]c^{2}[/tex] / [tex]2^{2}[/tex] + [tex]h^{2}[/tex] = [tex]10^{2}[/tex] / 4 + [tex]h^{2}[/tex] = 100
[tex]h^{2}[/tex] = 96
h = [tex]\sqrt{96}[/tex] = [tex]\sqrt{16 * 6}[/tex] = [tex]4\sqrt{6}[/tex]
Pb = [tex]\frac{a * h}{2}[/tex] = [tex]\frac{ 4 * 4\sqrt{6} }{2}[/tex] = [tex]8\sqrt{6}[/tex]
Pc = [tex]4\sqrt{3}[/tex] + 3 * [tex]8\sqrt{6}[/tex] = [tex]4\sqrt{3}[/tex] + [tex]24\sqrt{6}[/tex]
c)
a = 2
x = ?
[tex]a^{2}[/tex]+ [tex]b^{2}[/tex] = [tex]c^{2}[/tex] / [tex]1^{2}[/tex] + [tex]x^{2}[/tex] = [tex]2^{2}[/tex] / 1 + [tex]x^{2}[/tex] = 4
[tex]x^{2}[/tex] = 3
x = [tex]\sqrt{3}[/tex]
P = 1 * [tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex]
Pp = 6 * [tex]\sqrt{3}[/tex] = [tex]6\sqrt{3}[/tex]
h = ?
[tex]a^{2}[/tex]+ [tex]b^{2}[/tex] = [tex]c^{2}[/tex] / [tex]1^{2}[/tex] + [tex]h^{2}[/tex] = [tex]6^{2}[/tex] / 1 + [tex]h^{2}[/tex] = 36
[tex]h^{2}[/tex] = 35
h = [tex]\sqrt{35}[/tex]
Pb = [tex]\frac{2 * \sqrt{35} }{2}[/tex] = [tex]\sqrt{35}[/tex]
Pc = [tex]6\sqrt{3}[/tex] + 6 * [tex]\sqrt{35}[/tex] = [tex]6\sqrt{3}[/tex] + [tex]6\sqrt{35}[/tex]
O matko, na reszcie skończyłam, siedziałam nad tym z godzinę.
Z całym szacunkiem dla tego cudownego nauczyciela, który Ci to zadał, ale to wygląda jakby dał całkiem randomowe liczby i jestem ciekawa czy będąc w naszym wieku by to rozwiązał.
Cóż, mam nadzieję, że jest dobrze.
