[tex]m_a=\frac{a+b}{2} =2\sqrt{5}|*2 \\S=a+b=4\sqrt{5} \\S=3\sqrt{5} +b=4\sqrt{5} \\b=4\sqrt{5} -3\sqrt{5} =\sqrt{5} \\\\m_g=\sqrt{a*b} =\sqrt{3\sqrt{5}*\sqrt{5} } \\m_g=\sqrt{3\sqrt{25} } =\sqrt{3*5} =\sqrt{15}[/tex]
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[tex](a,b) d.p. (\sqrt{2} , \sqrt{8} )\\\sqrt{8} =2\sqrt{2} \\\\\frac{a}{\sqrt{2} } =\frac{b}{2\sqrt{2} } =k\\a=\sqrt{2} k\\b=2\sqrt{2} k\\\\m_g=\sqrt{a*b} =6\\a*b=6^2=36\\\sqrt{2} k*2\sqrt{2} k=36\\2\sqrt{4} k=36\\2*2k=36\\4k=36\\k=\frac{36}{4} =9\\\\a=\sqrt{2} k=9\sqrt{2} \\b=2\sqrt{2} k=18\sqrt{2} k[/tex]
