<s>[INST] Connecting midpoints of sides of a triangle In triangle $\triangle ABC$, $AB=8$, $BC=14$ and $CA=10$. Points $M$, $N$, and $P $ are the midpoints of sides $AB$, $BC$, and $CA$, respectively. If $M$, $N$, and $P$ are connected to form a triangle, what is the perimeter of triangle $\triangle MNP$?
 [/INST] 
$\displaystyle \frac{8}{14}=\frac{4}{MP}\Rightarrow MP=7$
$\displaystyle \frac{14}{8}=\frac{7}{NP}\Rightarrow NP=4$
$\displaystyle\frac{14}{10}=\frac{7}{MN}\Rightarrow MN=5$
Perimeter$=MP+NP+MN=7+4+5=16$
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