\({d}=\sqrt{2 {Rh}_{{T}}}+\sqrt{2 {Rh}_{{R}}}\)

\({d}=\sqrt{2 {R}}\left[\sqrt{{h}_{{T}}}+\sqrt{{h}_{{R}}}\right]\)

\({d}=\sqrt{2 {R}}[\sqrt{{x}}+\sqrt{160-{x}}]\)

\(\frac{{d}({d})}{{dx}}=0\)

\(\frac{1}{2 \sqrt{{x}}}+\frac{1(-1)}{2 \sqrt{160-{x}}}=0\)

\(\frac{1}{\sqrt{{x}}}=\frac{1}{\sqrt{160-{x}}}\)

\({x}=80\, {m}\)

\({d}_{\max }=\sqrt{2 \times 6400}\left[\sqrt{\frac{80}{1000}}+\sqrt{\frac{20}{1000}}\right]\)

\(=\frac{80 \sqrt{2} \times 2 \sqrt{80}}{10 \sqrt{10}}\)

\(=8 \times 2 \times \sqrt{2} \times 2 \sqrt{2}=64\, {km}\)