To find the length of one side of the rectangle, we know that opposite sides of a rectangle are equal in length. Therefore, we can set the two expressions for opposite sides equal to each other:

$5x + 2 = 47 - 4x$

Now, let's solve for $x$.

Step 1: Move all terms involving $x$ to one side.

Add $4x$ to both sides:

$5x + 4x + 2 = 47$ $9x + 2 = 47$

Step 2: Move the constant term to the other side.

Subtract 2 from both sides:

$9x = 45$

Step 3: Solve for $x$.

Divide both sides by 9:

$x = 5$

Step 4: Substitute $x = 5$ back into one of the side length expressions.

Substitute $x = 5$ into $5x + 2$:

$5(5) + 2 = 25 + 2 = 27 \, \text{cm}$

Thus, the length of one side of the rectangle is 27 cm.

Would you like further explanation on any part, or have more questions?

---

Here are some related questions to explore further:

1. What is the area of this rectangle?
2. How would you calculate the perimeter of this rectangle?
3. What happens if we change the value of $x$ to 6 in the side length expressions?
4. How would the solution change if the sides were described as unequal (e.g., 5x + 2 cm and 3x + 4 cm)?
5. How would you solve a similar problem if the side lengths involved quadratics?

Tip: Always check if the expressions for opposite sides are equal before proceeding with solving!