To find the height of the right rectangular prism, we can use the formula for the volume of a rectangular prism, which is:
\[ V = l \times w \times h \]
where \( V \) is the volume, \( l \) is the length, \( w \) is the width, and \( h \) is the height.
We know that:
- The volume \( V = 1.5 , \text{in}^3 \)
- The product of the length and width \( l \times w = 1.5 , \text{in}^2 \)
We can substitute \( l \times w \) into the volume formula:
\[ 1.5 = (l \times w) \times h \]
Substituting \( l \times w = 1.5 \):
\[ 1.5 = 1.5 \times h \]
To solve for \( h \), we divide both sides by \( 1.5 \):
\[ h = \frac{1.5}{1.5} = 1 \]
Thus, the height of the rectangular prism is:
\[ \boxed{1 , \text{in.}} \]