Final answer:
The height of the rectangular prism is calculated using the volume formula for a rectangular prism by dividing the given volume by the product of its length and width. The height is found to be 5/2 inches or 2.5 inches.
Step-by-step explanation:
To find the height of the rectangular prism, we use the formula for the volume of a rectangular prism, which is length × width × height. Given that the volume of the prism is 5/9 cubic inch, the length is 5/9 inch, and the width is 2/5 inch, we can set up the equation:
Volume = length × width × height
5/9 = (5/9) × (2/5) × height
Now, we solve for the height:
Height = (5/9) ÷ ((5/9) × (2/5))
Height = (5/9) ÷ (2/9)
Height = (5 ÷ 2)
Height = 5/2 inches
Therefore, the height of the prism is 5/2 inches or 2.5 inches.