20. The real numbers $x$ and $y$ satisfy the equations $4^y=\dfrac{1}{8(\sqrt2)^{x+2}}$ and $4^y=\dfrac{1}{8(\sqrt2)^{x+2}}$.

What is the value of $5^{x+y}$?

22. A square with perimeter 4 cm can be cut into two congruent right-angled triangles and two congruent trapezia as shown in the first diagram in such a way that the four pieces can be rearranged to form the rectangle shown in the second diagram.

What is the perimeter, in centimetres, of this rectangle?

24. In the diagram shown, $M$ is the mid-point of $PQ$. The line $PS$ bisects $\angle{RPQ}$ and intersects $RQ$ at $S$. The line $ST$ is parallel to $PR$ and intersects $PQ$ at $T$.

The length of $PQ$ is 12 and the length of $MT$ is 1. The angle $SQT$ is $120^\circ$.

What is the length of $SQ$ ?