Explanation:

- The volume of the cuboid is given as 3600 cubic cm.

- Areas of two adjacent faces are 225 square cm (let's say face 1) and 144 square cm (let's say face 2).

- Let the dimensions of the cuboid be a, b, and c such that \(a \times b = 225\), \(b \times c = 144\), and \(a \times b \times c = 3600\).

- To find the area of the other adjacent face, calculate \(a \times c\).

- Using these equations:

$$

a = \frac{225}{b},\ c = \frac{144}{b},\ \text{and from the volume}\ a \times b \times c = 3600.

$$

- Substitute these into the volume equation:

$$

\frac{225}{b} \times b \times \frac{144}{b} = 3600.

$$

- Solve for \(a \times c\):

$$

a \times c = \frac{3600}{b}.

$$

- Substitute values:

$$

b = \sqrt{\frac{225 \times 144}{3600}}.

$$

- Find the area \(a \times c = \frac{3600}{b}\).

- Calculations show area of the other face is 400 square cm.\n

- $$\textcolor{green}{\checkmark}\ \textbf{400 square cm is correct.}$$