To solve this, we can apply the Pythagorean Theorem. The room is rectangular, so the two walls and the diagonal form a right triangle. Let’s label the dimensions:

• The length of one wall is 3 meters (given).
• The length of the diagonal is 5 meters (given).
• We need to find the length of the other wall, which we'll call $x$.

According to the Pythagorean Theorem, for a right triangle with legs $a$ and $b$ and hypotenuse $c$, the relationship is:

$a^2 + b^2 = c^2$

In this case:

• $a = 3$ meters (one wall),
• $b = x$ meters (the other wall we need to find),
• $c = 5$ meters (the diagonal).

Substituting these values into the equation:

$3^2 + x^2 = 5^2$

Simplifying:

$9 + x^2 = 25$

Now, subtract 9 from both sides:

$x^2 = 16$

Taking the square root of both sides:

$x = 4$

So, the length of the other wall is 4 meters.

Would you like to dive deeper into how the Pythagorean theorem works or have any other questions? Here are some related questions:

1. What if the diagonal had been longer or shorter, how would the other wall change?
2. How would this apply if the room was not rectangular but a different shape?
3. What is the general formula for finding the diagonal of a rectangle?
4. Could we use trigonometry to solve this instead of the Pythagorean theorem?
5. What are some real-world applications where the Pythagorean theorem is used?

Tip: Always check if a problem involves a right triangle when you see two sides and a diagonal; it’s a perfect case for the Pythagorean Theorem!