To find the height of the right rectangular prism, we can use the formula for the volume of a rectangular prism, which is given by:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Let \( L \) be the length, \( W \) be the width, and \( H \) be the height. From the problem, we know:
- The volume \( V \) is \( 1.5 , \text{in}^3 \).
- The product of the length and width \( L \times W = 1.5 , \text{in}^2 \).
We can substitute \( L \times W \) in the volume formula:
\[ V = (L \times W) \times H \]
Substituting the known values:
\[ 1.5 = 1.5 \times H \]
To find \( H \), we can divide both sides by \( 1.5 \):
\[ H = \frac{1.5}{1.5} = 1 , \text{in} \]
Thus, the height of the prism is
\[ \boxed{1 , \text{in}} \]