To find the height of the right rectangular prism, we can use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Let's denote the length as \( L \), the width as \( W \), and the height as \( H \). According to the problem, we have:
\[ L \times W = 1.5 , \text{in}^2 \] \[ L \times W \times H = 1.5 , \text{in}^3 \]
From the volume formula, we can substitute \( L \times W \) with \( 1.5 , \text{in}^2 \):
\[ 1.5 , \text{in}^2 \times H = 1.5 , \text{in}^3 \]
To find \( H \), we can divide both sides by \( 1.5 , \text{in}^2 \):
\[ H = \frac{1.5 , \text{in}^3}{1.5 , \text{in}^2} = 1 , \text{in} \]
Thus, the height of the prism is:
\[ \boxed{1 , \text{in}} \]