In rectangle ABCD, AB = 3x and BC = 4x. Find the length of AC and BD in terms of x.

In a rectangle, all angles are $90^\circ$. Therefore, $\triangle ABC$ is a right-angled triangle with the right angle at B. The diagonals of a rectangle are also equal in length, so $AC = BD$.

In $\triangle ABC$:

Substitute the given values $AB = 3x$ and $BC = 4x$:

Take the square root of both sides:

Since the diagonals of a rectangle are equal in length:

The length of AC is $\boxed{\mathbf{5x}}$ and the length of BD is $\boxed{\mathbf{5x}}$.