In $\Delta ABC$,$m \angle B = 90^{\circ}$. If $AB = 20$ and $AC = 29$,find the perimeter of $\Delta ABC$.

$A$ and $B$ are points on the sides $PQ$ and $PR$ of a triangle $PQR$ respectively,such that $PQ = 12.5 \, cm$,$PA = 5 \, cm$,$BR = 6 \, cm$,and $PB = 4 \, cm$. Is $AB \parallel QR$? Give reasons for your answer.

In $\Delta PQR$,$m \angle P = m \angle Q + m \angle R$. If $PQ = 20$ and $QR = 25$,then the perimeter of $\Delta PQR$ is............

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM : MB = 4 : 13$ and $AC = 20.4$,find $AN$.

In $\Delta ABC$,$A-P-B$,$A-Q-C$ and $\overline{PQ} \parallel \overline{BC}$. Then,$\ldots \ldots \ldots$ holds good.

Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle,write the length of its hypotenuse.
$13\, cm, 12\, cm, 5\, cm$