If the volume of a right rectangular prism is 1.5in and its length and width have a product of 1.5 in, what is the height of this prism
Let's call the length of the rectangular prism "l", the width "w", and the height "h". We know that the volume of the prism is 1.5 cubic inches, so:
V = lwh = 1.5
We also know that the product of the length and width is 1.5 square inches, so:
lw = 1.5
We can solve for one of the variables in terms of the other two by rearranging these equations. Let's solve for "h" in terms of "l" and "w":
h = V/lw = 1.5/(lw)
Now we can substitute the given value for lw:
h = 1.5/(1.5) = 1 inch
So the height of the right rectangular prism is 1 inch.
To find the height of the right rectangular prism, we can use the formula for the volume of a rectangular prism:
Volume = length x width x height
We are given that the volume of the prism is 1.5 in³ and that the length and width have a product of 1.5 in. Let's assign variables to the length, width, and height:
Length = L
Width = W
Height = H
Given:
Volume = 1.5 in³
Length x Width = 1.5 in
We can write the equation for the volume in terms of these variables:
1.5 = L x W x H
Now let's substitute the given information into the equation:
1.5 = 1.5 x H
Divide both sides of the equation by 1.5:
H = 1
Therefore, the height of the right rectangular prism is 1 inch.