In $\Delta ABC,$ $\overline{AD}$ is a median. If $AD=7,$ $AC=7$ and $BD=4,$ find the perimeter of $\Delta ABC.$

In $\Delta PQR$,$m\angle Q = 90^{\circ}$,$PR = a^{2} + b^{2}$ and $QR = a^{2} - b^{2}$. Then,$PQ = \ldots$ $(a, b \in R^{+}; a > b)$

$\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow XYZ$. If $AB : XY = 4 : 5$ and $AC = 6$,then $XZ = \ldots$

In quadrilateral $ABCD$,a line through $A$ intersects $BD$ at $L$,$CD$ at $M$,and the extension of $BC$ at $N$. Prove that $\frac{LD^2}{LB^2} = \frac{LM}{LN}$.

In $\Delta ABC$,$m\angle B = 90^{\circ}$. If $a = 16$ and $c = 12$,then $b = \ldots$

$\Delta DEF$ and $\Delta PQR$ are similar triangles if $m \angle D = m \angle R$ and $\ldots \ldots$