If the volume of a right rectangular prism is 1.5in^3 and its length and width have a product of 1.5in^3 and its length and width have a product of 1.5^2 what is the height of this prism
To find the height of the prism, we can use the formula for the volume of a rectangular prism:
Volume = Length x Width x Height
Given that the volume is 1.5in^3 and the product of the length and width is 1.5^2, we can rewrite these relationships as:
1.5 = Length x Width x Height
1.5^2 = Length x Width
Since the product of the length and width is 1.5^2, we can rewrite this as:
Width = 1.5^2 / Length
Substitute this expression for the width into the volume equation:
1.5 = Length x (1.5^2 / Length) x Height
1.5 = 1.5 Height
Divide by 1.5 on both sides:
Height = 1in
Therefore, the height of the right rectangular prism is 1 inch.