If $\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR$,and given $AB + BC = 12$,$PQ + QR = 15$,and $AC = 8$,find the length of $PR$.

Below are given the measures of sides $\overline{PQ}$,$\overline{QR}$ and $\overline{PR}$ of $\Delta PQR$. In each case,determine whether $\Delta PQR$ is a right-angled triangle or not. If it is a right-angled triangle,state which angle is a right angle: $PQ = 8, QR = 6, PR = 12$.

The length of a diagonal of a square is $8 \sqrt{2}$. Then,the perimeter of the square is..............

$\square XYZW$ is a rectangle. If $XY + YZ = 17$ and $XZ + YW = 26$,find $XY$ and $YZ$ (given $XY > YZ$).

The area of an equilateral triangle is $36 \sqrt{3}$. Find the measure of its sides.

In $\Delta XYZ$,$\overline{XN}$ is a median. If $XY^2 + XZ^2 = 200$ and $XN = 8$,find $YZ$.