Consideremos o triângulo NPM reto em P.
$\,\left.\begin{array}{rcr} \mbox{cateto menor } \phantom{X}\;\,\rightarrow\, & \;\;\overline{PM}\,=\,\dfrac{\sqrt{2}}{2}\mbox{ cm }\; \\ \,\mbox{cateto maior }\phantom{XX} \rightarrow\, & \overline{NP}\,=\,\dfrac{3}{2}\mbox{ cm}\\ \mbox{teorema de Pitágoras}\, \rightarrow\, & (\overline{MN})^{\large 2}\,=\,(\overline{MP})^{\large 2}\,+\,(\overline{NP})^{\large 2}\; \\ \end{array} \right\}\;\Rightarrow\;$
$\;\Rightarrow\;(\overline{MN})^{\large 2}\,=\,(\dfrac{\sqrt{2}}{2})^{\large 2}\,+\,(\dfrac{3}{2})^{\large 2}\;\Leftrightarrow\;\boxed{\;\overline{MN}\,=\,\dfrac{\sqrt{11}}{2} \mbox{ cm}\;}$