[tex]5a)c= \sqrt{144+144}= \sqrt{2*144} =12 \sqrt{2}cm \\ 5b)c= \sqrt{162+162}= \sqrt{2*162}= \sqrt{4*81}=18 cm \\ 5c)c= \sqrt{x^2+ x^{2} } = \sqrt{2x^2}=x \sqrt{2 } \\ 6a)d=a \sqrt{2}=8 \sqrt{2};b)d=15 \sqrt{2}* \sqrt{2}=30;c)d=x \sqrt{2} \\ 7a)h= \sqrt{16-4}=2 \sqrt{3}cm;b)h= \sqrt{108-27}=9cm; [/tex]
[tex]c)h= \sqrt{x^2- \frac{x^2}{4} }= \frac{x \sqrt{3} }{2} \\ 8a) x^{2} + x^{2} =(18 \sqrt{2})^2 \\ 2 x^{2} =324*2 \\ a \sqrt{2}=20 \\ a= \frac{ 20}{ \sqrt{2} } = 10 \sqrt{2 } \\ c) x^{2}=54+ \frac{x^2}{4} \\ \frac{3x^2}{4}=54 \\ x^{2} =4*18 \\ x=6 \sqrt{2} [/tex]
[tex]9a)AB= \sqrt{AC^2+BC^2}= \sqrt{144+25}=13cm \\ b)BC= \sqrt{AB^2-AC^2}= \sqrt{400-256}=12cm \\ c)AC= \sqrt{AB^2-BC^2}= \sqrt{41^2-40^2}=9cm [/tex]
