To find the length of the diagonal of a rectangular prism, we can use the formula for the space diagonal \( d \):
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.
Given:
- Length \( l = 4 , \text{cm} \)
- Width \( w = 3 , \text{cm} \)
- Height \( h = 12 , \text{cm} \)
Now, substituting the values into the formula:
\[ d = \sqrt{(4)^2 + (3)^2 + (12)^2} \]
Calculating each square:
\[ = \sqrt{16 + 9 + 144} \]
\[ = \sqrt{169} \]
\[ = 13 \]
Thus, the length of the diagonal of the prism is \( \boxed{13} \).
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