Answer:
5/3 inches
Explanation:
To find the height of the rectangular prism, we can use the formula for the volume of a rectangular prism: Volume = Length × Width × Height.
Given:
Length = 5/6 inch
Width = 2/5 inch
Volume = 5/9 cubic inch
Let's assume the height of the prism is "h" inches.
Using the formula for volume, we can set up the equation:
(5/6) × (2/5) × h = 5/9
Now, let's solve for h:
(10/30) × h = 5/9
Multiplying both sides of the equation by 30 to get rid of the denominators:
10h = 5/9 × 30
10h = 150/9
To simplify the right side, we can divide both the numerator and denominator by their greatest common divisor, which is 3:
10h = (150/3) ÷ (9/3)
10h = 50/3
Dividing both sides by 10:
h = (50/3) ÷ 10
h = 5/3
Therefore, the height of the prism is 5/3 inches.