5. The lengths of the adjacent sides of a rectangle are $\sqrt{404} \mathrm{~cm}$ and $\sqrt{909} \mathrm{~cm}$. Determine the perimeter and the area of the circle circumscribed around a square whose area is equal to the area of the given rectangle.
5. The area of the given rectangle is equal to the product of the lengths of its adjacent sides, that is

$P_{1}=\sqrt{404} \cdot \sqrt{909}=\sqrt{4 \cdot 101} \cdot \sqrt{9 \cdot 101}=2 \sqrt{101} \cdot 3 \sqrt{101}=6 \cdot 101=606 \mathrm{~cm}^{2} . \quad 1 \mathrm{BOD}$

Let the length of the side of a square that has the same area as the given rectangle be $a$.

Then $a^{2}=606$ and $a=\sqrt{606} \mathrm{~cm}$.

$1 \mathrm{BOD}$

The length of the diagonal of this square is $d=a \sqrt{2}=\sqrt{606} \cdot \sqrt{2}=\sqrt{606 \cdot 2}=\sqrt{303 \cdot 2 \cdot 2}=2 \sqrt{303} \mathrm{~cm}$.

$1 \mathrm{BOD}$

The radius of the circle circumscribed around this square is $r=\frac{d}{2}=\frac{2 \sqrt{303}}{2}=\sqrt{303} \mathrm{~cm}$.

1 BOD

The circumference of this circle is $\mathrm{O}=2 r \pi=2 \sqrt{303} \pi \mathrm{cm}$,

1 BOD and the area is $P_{2}=r^{2} \pi=(\sqrt{303})^{2} \pi=303 \pi \mathrm{cm}^{2}$