To find the height of the right rectangular prism, we can use the formula for the volume of a rectangular prism:
\[ V = \text{length} \times \text{width} \times \text{height} \]
We are given that the volume \( V = 1.5 , \text{in}^3 \) and that the product of the length and width is:
\[ \text{length} \times \text{width} = 1.5 , \text{in}^2 \]
Let \( L \) be the length and \( W \) be the width. Thus, we have:
\[ L \times W = 1.5 , \text{in}^2 \]
Now we substitute this product into the volume formula:
\[ 1.5 = (L \times W) \times \text{height} \]
Substituting \( L \times W \) gives us:
\[ 1.5 = 1.5 \times \text{height} \]
To find the height, we can divide both sides by \( 1.5 \):
\[ \text{height} = \frac{1.5}{1.5} = 1 \]
Therefore, the height of the rectangular prism is
\[ \boxed{1} , \text{in.} \]