You seem to be describing two squares, but squares have all sides of equal length. It sounds like you're actually referring to rectangles.

Let's assume the first "square" is a rectangle with a length of 15 and a width of 9, and the second "square" is a rectangle with a length of $x$ and a width of 4.

If the problem asks for $x$, it could be that the two rectangles are supposed to be proportional or similar. Rectangles are similar if their corresponding sides are in proportion. For two rectangles to be similar:

$\frac{\text{Length}_1}{\text{Width}_1} = \frac{\text{Length}_2}{\text{Width}_2}$

Using the given values:

$\frac{15}{9} = \frac{x}{4}$

To find $x$, cross-multiply and solve for $x$:

[ 15 \times 4 = 9