[tex]Avem:
\texttt{Dreptunghiul MNPQ in care:} \\
\texttt{MP = 10 cm = diagonala lui MNPQ si ipotenuza } \Delta NMP \\
\texttt{MN = 8 cm = lungimea lui MNPQ si cateta } \Delta NMP \\ \\
\texttt{a) Calculam NP = latimea lui MNPQ si cateta } \Delta NMP \\ \\
NP = \sqrt{MP^2 - MN^2}= \sqrt{10^2 - 8^2}= \sqrt{100 - 64}=\sqrt{36}=\boxed{6~cm} \\ \\
\texttt{Calculam perimetrul dreptunghiului MNPQ.} \\ \\
P= 2(L + l) = 2(MN + NP) = 2(8 + 6) =2 \times 14 = \boxed{28 ~cm}
[/tex]
[tex] \displaystyle \\
\texttt{b) Calculam d(N, MP)} \\
\texttt{d(N, MP) este inaltimea ipotenuzei in }\Delta MNP \\ \\
d(N, MP) = \frac{\texttt{Produsul catetelor}}{\texttt{Ipotenuza}} \\ \\ d(N, MP) = \frac{MN \times NP}{MP}=\frac{8 \times 6}{10}= \frac{48}{10}= \boxed{\frac{24}{5}~cm} = \boxed{4,8 ~cm}[/tex]
