The side lengths, in units, of triangle $MNO$ are given.

${MN}=5$

${NO}=4$

${OM}=2.5$

Triangle $MNO$ is dilated by a scale factor of $k$, with the center at point $M$, to create triangle $MGH$. Triangle $MGH$ has a perimeter of $17.25$ units.

What is the value of $k$ ?