#### Answer

$x = 3$
All sides must have a length of $15$.

#### Work Step by Step

All sides of a rhombus are congruent, so let us take two of the sides and set them equal to one another so we can find the value of one of the variables:
$4x + 3 = 15$
Subtract $3$ from each side of the equation to move constants to the right side of the equation:
$4x = 12$
Divide each side of the equation by $4$ to solve for $x$:
$x = 3$
Now, we set the two other opposite sides equal to one another:
$3y = 5x$
Plug in $3$ for $x$:
$3y = 5(3)$
Multiply to simplify:
$3y = 15$
Divide each side by $3$ to solve for $y$:
$y = 5$
If this is a rhombus, then all sides are congruent; therefore, we can deduce that all sides must have a length of $15$, which is given as the length of one of the sides.