If the volume of a right rectangular prism is 1.5in.3 and it's length and width have a product of 1.5in.2 , what is the height of the prism?
To find the height of the prism, we need to use the formula for the volume of a rectangular prism, which is:
Volume = Length x Width x Height
Given that the volume is 1.5in^3 and the product of the length and width is 1.5in^2, we can write two equations:
1.5 = 1.5 x height (equation for volume)
1.5 = length x width (equation for product of length and width)
Since the product of the length and width is 1.5in^2, we can represent this as:
length = 1.5 / width
Substitute this expression for length into the equation for volume:
1.5 = (1.5 / width) x width x height
1.5 = 1.5 x height
The units cancel out, so we are left with:
1 = height
Therefore, the height of the prism is 1 inch.