In rectangle $HIJK$,$HJ = 13$ and $HI = 5$. Then,the perimeter of rectangle $HIJK$ is.......

In $\Delta XYZ$,$P$ and $Q$ are the midpoints of $\overline{XY}$ and $\overline{XZ}$ respectively. If the area of $\Delta XYZ$ is $140$,find the area of $\Delta XPQ$.

Given $\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR$. If $2 m \angle P = 3 m \angle Q$ and $m \angle C = 100^{\circ}$,find $m \angle B$. (in $^{\circ}$)

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BD}$ is an altitude to the hypotenuse $\overline{AC}$. Then,the correspondence $ABC \leftrightarrow \ldots$ between $\Delta ABC$ and $\Delta ADB$ is a similarity.

Legs (sides other than the hypotenuse) of a right triangle are of lengths $16 \,cm$ and $8 \,cm$. Find the length of the side of the largest square that can be inscribed in the triangle. (in $cm$)

In $\Delta ABC,$ the bisectors of $\angle B$ and $\angle C$ intersect $\overline{AC}$ and $\overline{AB}$ at $D$ and $E$ respectively. If $\overline{DE} \parallel \overline{BC},$ prove that $\Delta ABC$ is an isosceles triangle.