[tex] \frac{a}{2} = \frac{b}{5} = \frac{c}{6} = k \\ a = 2k \\ b = 5k \\ c = 6k \\ ab + bc + ca = 208 \\ 2k \times 5k + 5k \times 6k + 6k \times 2k =208 \\ 10k^{2} + 30k^{2} + 12k ^{2} =208 \\ 52k ^{2} = 208 \\ k ^{2} = 208 \div 52 \\ k ^{2} = 4 \\ k = \ \sqrt{4} \\ k = 2 \\ a = 2k = 2 \times 2 = 4 \\ b = 5k = 5 \times 2 = 10 \\ c = 6k = 6 \times 2 = 12[/tex]
