a) [latex] c^{2} [/latex] + ([latex] frac{1}{2} [/latex]a) ^2 = [latex] k^{2} [/latex] [latex] c^{2} + 4 ^{2} = 7^{2} [/latex] [latex] c^{2} +16=49[/latex] [latex] c^{2} = 33[/latex] c=[latex] sqrt{33} [/latex] b) [latex]d= frac{1}{2}a sqrt{2} = frac{1}{2} 6 sqrt{2} =3 sqrt{2} [/latex] x=d [latex] H^{2} + x^{2} = k^{2} [/latex] [latex] H^{2} + (3 sqrt{2} )^2 = 8^{2} [/latex] [latex]H ^{2} +18=64[/latex] [latex] H^{2} =46[/latex] H=[latex] sqrt{46} [/latex] c) [latex] k^{2} = H^{2} + b^{2} [/latex] [latex] (sqrt{33})^2 = 5^{2} + b^{2} [/latex] [latex]33=25+b[/latex] [latex] b^{2} = 33-25[/latex] [latex]b ^{2} = 8[/latex] [latex]b=2 sqrt{2} [/latex] [latex]b= frac{1}{2} d[/latex] [latex][latex] 2sqrt{2} = frac{1}{2} d |*2[/latex] [latex] 4sqrt{2} =d[/latex] [latex]d= 4sqrt{2} [/latex] [latex]d= asqrt{2} [/latex] [latex] 4sqrt{2} = asqrt{2} | : sqrt{2} \ a=4[/latex]
