The area \( A \) of a rhombus can be calculated using the lengths of its diagonals \( d_1 \) and \( d_2 \) with the formula:
\[ A = \frac{1}{2} d_1 d_2 \]
In this problem, we are given that one diagonal \( d_1 \) is 8 cm, and the area \( A \) is 72 square centimeters. We need to find the length of the other diagonal \( d_2 \).
Substituting the known values into the area formula, we have:
\[ 72 = \frac{1}{2} (8) d_2 \]
To isolate \( d_2 \), we can first multiply both sides of the equation by 2 to eliminate the fraction:
\[ 144 = 8 d_2 \]
Next, we divide both sides by 8:
\[ d_2 = \frac{144}{8} = 18 \]
Thus, the length of the other diagonal \( d_2 \) is:
\[ \boxed{18} \text{ cm} \]
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