[tex]a)\\\\2^{2} +h^{2} =4^{2} \\\\h^{2} =16-4\\\\h^{2} =12\\\\h=\sqrt{12}=\sqrt{4*3} =2\sqrt{3} \\\\Ob = 2+4+2\sqrt{3}=6+2\sqrt{3}\\\\P=\frac{1}{2} *2*2\sqrt{3}=2\sqrt{3}[/tex]
[tex]b)\\ a\sqrt{2} =5\\\\a=\frac{5}{\sqrt{2} } = \frac{5*\sqrt{2}}{\sqrt{2} *\sqrt{2}}=\frac{5\sqrt{2}}{2}\\\\Ob=\frac{5\sqrt{2}}{2}+\frac{5\sqrt{2}}{2}+5 = \frac{10\sqrt{2}}{2} + 5=5\sqrt{2} +5\\\\P = \frac{1}{2} *\frac{5\sqrt{2}}{2}*\frac{5\sqrt{2}}{2}= \frac{25*2}{8} =\frac{50}{8}[/tex]
[tex]c)\\\\(\sqrt{2} )^{2} +4^{2} =c^{2} \\\\2+16=c^{2} \\\\c^{2} =18\\\\c=\sqrt{18} =\sqrt{9*2} =3\sqrt{2} \\\\Ob = \sqrt{2} +4+3\sqrt{2} =4+4\sqrt{2} \\\\P=\frac{1}{2} *\sqrt{2} *4=2\sqrt{2}[/tex]
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[tex]a)\\\\2^{2} +h^{2} =4^{2} \\\\h^{2} =16-4\\\\h^{2} =12\\\\h=\sqrt{12}=\sqrt{4*3} =2\sqrt{3} \\\\Ob = 2+4+2\sqrt{3}=6+2\sqrt{3}\\\\P=\frac{1}{2} *2*2\sqrt{3}=2\sqrt{3}[/tex]
[tex]b)\\ a\sqrt{2} =5\\\\a=\frac{5}{\sqrt{2} } = \frac{5*\sqrt{2}}{\sqrt{2} *\sqrt{2}}=\frac{5\sqrt{2}}{2}\\\\Ob=\frac{5\sqrt{2}}{2}+\frac{5\sqrt{2}}{2}+5 = \frac{10\sqrt{2}}{2} + 5=5\sqrt{2} +5\\\\P = \frac{1}{2} *\frac{5\sqrt{2}}{2}*\frac{5\sqrt{2}}{2}= \frac{25*2}{8} =\frac{50}{8}[/tex]
[tex]c)\\\\(\sqrt{2} )^{2} +4^{2} =c^{2} \\\\2+16=c^{2} \\\\c^{2} =18\\\\c=\sqrt{18} =\sqrt{9*2} =3\sqrt{2} \\\\Ob = \sqrt{2} +4+3\sqrt{2} =4+4\sqrt{2} \\\\P=\frac{1}{2} *\sqrt{2} *4=2\sqrt{2}[/tex]