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 $AC$.

$\square PQRS$ is a rectangle. $PQ + QR = 7$ and the area of $\square PQRS$ is $12$. Then,$PR = \ldots$

............... is not a condition for the similarity of two triangles.

In $\Delta ABC$,$\overline{AB} \cong \overline{AC}$ and $\overline{AM}$ is an altitude. If $AM = 15$ and the perimeter of $\Delta ABC$ is $50$,find the area of $\Delta ABC$.

In rhombus $ABCD$,$AC = 15$ and $BD = 36$. Find the perimeter of rhombus $ABCD$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AB = 3$ and $AC = 5$,find the length of $BM$.