The length of a diagonal of a square is $6$. Then, the length of its sides is $\ldots \ldots \ldots$ (in $\sqrt{2}$)

The length of a diagonal of a square is $12$. Then,the length of each side of the square is...........

$A$ street light bulb is fixed on a pole $6 \, m$ above the level of the street. If a woman of height $1.5 \, m$ casts a shadow of $3 \, m$,find how far she is away from the base of the pole. (in $m$)

The perimeter of square $ABCD$ is $20$. Find $AC$. (in $\sqrt{2}$)

In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle Q$ and $\angle B \cong \angle R$. Which correspondence between them is a similarity?

In $\Delta ABC$,$m\angle B = 90^\circ$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 4CM$,prove that $AB = 2BC$.