Find the Face Diagonal of a Rectangular Prism with Base Diagonal X and Length 3X

To solve this problem, we'll follow these steps:

• Step 1: Determine the side length of the square base
• Step 2: Calculate the diagonal of the rectangular face using the Pythagorean theorem

Now, let's work through each step:
Step 1: The side length $s$ of the square base is calculated from its diagonal $X$ as $s = \frac{X}{\sqrt{2}}$.
Step 2: The diagonal $d$ of the rectangular face is found using $d^2 = s^2 + (3X)^2$, which simplifies to $d = X\sqrt{9.5}$.

The solution to the problem is $x\sqrt{9.5}$.