Remember that
If two triangles are similar, then the ratio of its corresponding sides is proportional
In this problem
triangle ABC is similar to triangle PQR
that means
AB/PQ=BC/QR=AC/PR
so
AB/PQ=AC/PR
we have
AB=3.1 cm
PQ=QP=?
AC=9.8 cm
PR=RP=2.7 in
substitute given values
3.1/QP=9.8/2.7
Solve for QP
QP=(3.1*2.7)/9.8
QP=0.85 in