Let the length of the rectangle be $4x$ and the width be $3x$.
The perimeter of the rectangle is $2(4x+3x)=14x$.
We are given that the perimeter is 56, so $14x=56$ and $x=4$.
The length of the rectangle is $4x=4(4)=16$ meters and the width is $3x=3(4)=12$ meters.
Using the Pythagorean theorem, the length of the diagonal is $\sqrt{16^2+12^2}=\sqrt{256+144}=\sqrt{400}=20$ meters.
The answer is: 20
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
If the perimeter of a rectangle is 56 meters and the ratio of its length to its width is 4:3, what is the length in meters of the rectangle's diagonal?

### Answer:
