A square has a side length of (3x + 5) cm and also (2x + 9) cm. Find the area of the square.

$$3x + 5 = 2x + 9$$

Subtract $2x$ from both sides:

$$3x - 2x + 5 = 9$$ $$x + 5 = 9$$

Subtract 5 from both sides:

$$x = 9 - 5$$ $$x = 4$$

Using the expression $(3x + 5)$ cm:

$$Side = 3(4) + 5$$ $$Side = 12 + 5$$ $$Side = 17 \text{ cm}$$

(Alternatively, using $(2x + 9)$ cm: $2(4) + 9 = 8 + 9 = 17$ cm. Both give the same result.)

The area of a square is given by the formula $Area = Side \times Side$.

$$Area = 17 \text{ cm} \times 17 \text{ cm}$$ $$Area = 289 \text{ cm}^2$$

The area of the square is $\boxed{\text{289 cm}^2}$.