The diagonal of a square is $15 \mathrm{m}$ find the length of its one side and perimeter.

The perimeter of a square is numerically equal to its area. Find its area.

Each side of a rectangle is doubled. Find the ratio between: 

Perimeters of the original rectangle and the resulting rectangle.

Each side of a rectangle is doubled. Find the ratio between:

Areas of the original rectangle and the resulting rectangle.

In the following case ABCD is a square and PQRS is a rectangle. If the area of the shaded portion is $k {\mathrm{m}}^2$, find $k$.

(All measurements are in meter)

In the following case ABCD is a square and PQRS is a rectangle. If the area of the shaded portion is $k {\mathrm{m}}^2$, find $k$.

(All measurements are in meter)