To find the height of the right rectangular prism, you can use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
You've given the volume as \(3.5 , \text{in}^3\) and the product of the length and width as \(2.8 , \text{in}^2\).
Let:
- \( l \) = length
- \( w \) = width
- \( h \) = height
From the information provided, we have:
\[ l \times w = 2.8 , \text{in}^2 \]
Now, substituting the known values into the volume formula:
\[ 3.5 = (l \times w) \times h \]
Now substitute \( l \times w \) with \( 2.8 \):
\[ 3.5 = 2.8 \times h \]
To find \( h \), divide both sides by \( 2.8 \):
\[ h = \frac{3.5}{2.8} \]
Calculating this:
\[ h = 1.25 , \text{in} \]
So, the height of the rectangular prism is \( \boxed{1.25 , \text{in}} \).