In $\Delta XYZ, m\angle Y = 90^{\circ}$. If $XY = YZ$ and $XZ = 10$,then $XY = \ldots$

The heights of two poles standing erect on a flat ground are $6 \, m$ and $11 \, m$. If the distance between their bases is $12 \, m$,find the distance between their tops.

$...$ correspondences of an equilateral triangle with itself are similarity.

Find the value of $x$ for which $DE \parallel AB$ in the given figure.

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QS}$ is an altitude. If $PS - SR = 10$ and $PQ^2 - QR^2 = 260$,then $PR = \dots$

If $\Delta ABC \sim \Delta DEF$ for the correspondence $ABC \leftrightarrow DEF$,and given $AB = 8$,$AC = 10$,$DE = 12$,and $EF = 18$,find the perimeter of $\Delta DEF$.