${\left(50\text{cm}\right)}^2+{\left(30\text{cm}\right)}^2={\left|AB\right|}^2$  

$2500{\text{cm}}^2+900{\text{cm}}^2={\left|AB\right|}^2$  

$3400{\text{cm}}^2={\left|AB\right|}^2\mid \sqrt{}$  

${\left|AB\right|}^2=3400{\text{cm}}^2\mid \sqrt{}$  

$\left|AB\right|=\sqrt{3400}\text{cm}=\sqrt{34\cdot 100}\text{cm}=\sqrt{34}\cdot \sqrt{100}\text{cm}=\sqrt{34}\cdot 10\text{cm}=10\sqrt{34}\text{cm}$