In $\Delta PQR$,$\overline{PM}$ is a median. If $PQ^{2} + PR^{2} = 148$ and $PM = 7$,find $QR$.

In square $ABCD$,$AB = 4 \sqrt{2}$. Then,the length of a diagonal of the square is......

The ratio of corresponding sides of two similar triangles is $4:9$. Then,the ratio of their areas is $\ldots \ldots \ldots \ldots$

In $\Delta ABC$,$M$ lies on $AB$ and $N$ lies on $AC$ such that $\overline{MN} \parallel \overline{BC}$. If $AM = 6$,$MB = 9$,and $AN = 8$,find $AC$.

$\Delta PQR \sim \Delta DEF$ for the correspondence $PQR \leftrightarrow DEF$. If $3 PQ = 2 DE$,$EF = 6$,and $PR = 8$,find $QR$ and $DF$.

The perimeter of rectangle $ABCD$ is $28$. If $AC = 10$ and $AB < BC$,find the measures of its sides.