1.
a)
[tex]2^2+4^2=x^2\\4+16=x^2\\x = \sqrt{20}\\x = 2\sqrt5[/tex]
b)
[tex]5^2+x^2=20^2\\x^2=400-25\\x^2=375\\x=\sqrt{5*5*15} = 5\sqrt{15}\\[/tex]
c)
[tex]x^2+20^2=34^2\\x^2=1156-400\\x^2=756\\x=\sqrt{756}=\sqrt{2*2*3*3*21}\\x = 6\sqrt{21}[/tex]
2.
[tex]5^2+10^2=y^2\\y^2=100+25\\y^2=125\\y=5\sqrt5[/tex]
Na podstawie podobieństwa trójkątów:
[tex]\frac5{10}=\frac{5+6}y\\5=\frac{110}{y}\\5y=110\\y=22[/tex]
