Đáp án:
$24(cm)$
Giải thích các bước giải:
$\Delta MNP$ vuông tại $M$, đường cao $MK$
$\Rightarrow \left\{\begin{array}{l} MN.MP=MK.NP\\ MN^2+MP^2=NP^2\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} MN.MP=48\\ MN^2+MP^2=100\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} MN=\dfrac{48}{MP}\\ \dfrac{2304}{MP^2}+MP^2=100\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} MN=\dfrac{48}{MP}\\ 2304+MP^4=100MP^2\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} MN=\dfrac{48}{MP}\\ MP^4-100MP^2+2304\end{array} \right.\\ \Leftrightarrow \left\{\begin{array}{l} MN=\dfrac{48}{MP}\\ \left[\begin{array}{l} MP^2=64\\ MP^2=36\end{array} \right.\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} \left\{\begin{array}{l} MN=6\\ MP=8\end{array} \right.\\\left\{\begin{array}{l} MN=8\\ MP=6\end{array} \right.\end{array} \right.$
Chu vi $\Delta MNP: MN+MP+NP=6+8+10=24(cm)$
