To find the height of the rectangular ink pad, we can use the formula for the perimeter of a rectangle:
\[ P = 2 \times (\text{length} + \text{width}) \]
In this case, we know the perimeter \( P = 46 \) cm and the width is \( 13 \) cm. Let's denote the height (or length) as \( h \). We can set up the equation as follows:
\[ 46 = 2 \times (h + 13) \]
Now, we can simplify and solve for \( h \):
- Divide both sides by 2:
\[ 23 = h + 13 \]
- Subtract 13 from both sides:
\[ h = 23 - 13 \]
\[ h = 10 \]
Thus, the height of the ink pad is \( \boxed{10} \) centimeters.
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