We wszystkich zadaniach wykorzystujemy tw. Pitagorasa.
Zadanie 2.
a)
[tex]h^2+(\sqrt{7})^2=7^2\\
h^2+7=49\\
h^2=42\\
a^2+h^2=8^2\\
a^2+42=64\\
a^2=22\\
a=\sqrt{22}[/tex]
b)
[tex](b+3,8\sqrt{2})^2=(7+5)^2+(3\sqrt{2})^2\\
(b+3,8\sqrt{2})^2=144+18=162\\
b+3,8\sqrt{2}=\sqrt{162}=\sqrt{81*2}=9\sqrt{2}\\
b=9\sqrt{2}-3,8\sqrt{2}=5,2\sqrt{2}[/tex]
Zadanie 3.
a)
[tex]a=6\\
\frac{1}{2} e=3\sqrt{3}\\
e=6\sqrt{3}\\
(\frac{1}{2} f)^2+(\frac{1}{2} e)^2=6^2\\
(\frac{1}{2} f)^2+(3\sqrt{3})^2=6^2\\
(\frac{1}{2} f)^2+27=36\\
(\frac{1}{2} f)^2=9\\
\frac{1}{2} f=3\\
f=6\\
P=\frac{e*f}{2} =\frac{6\sqrt{3}*6}{2}=18\sqrt{3}\\
Obw=4a=4*6=24[/tex]
b)
[tex]h^2+15^2=17^2\\
h^2+225=289\\
h^2=64\\
h=8\\
a=15+10+15=40\\
P=\frac{(a+b)*h}{2}=\frac{(40+10)*8}{2}=200\\
Obw=a+b+2c=40+10+2*17=84[/tex]
