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,
- \(h\) is the height.
According to the problem, we have the following information:
- Volume \(V = 1.5 , \text{in}^3\)
- The product of the length and width \(l \times w = 1.5 , \text{in}^2\)
Now, we can express the height \(h\) in terms of the volume and the product of length and width:
\[ h = \frac{V}{l \times w} \]
Substituting the provided values into the equation:
\[ h = \frac{1.5 , \text{in}^3}{1.5 , \text{in}^2} \]
Calculating this:
\[ h = 1 , \text{in} \]
Thus, the height of the prism is:
\[ \boxed{1 , \text{in}} \]