If the volume of a right rectangular prism is 1.5 in.3 and its length and width have a product of 1.5 in.2, what is the height of this prism?
Let the length of the rectangular prism be L, the width be W, and the height be H.
We know that the volume of the prism is 1.5 in.3:
V = LWH = 1.5
We are also given that the product of the length and width is 1.5 in.2:
LW = 1.5
We can use this information to solve for H:
H = V/LW = 1.5/(LW)
Substituting LW = 1.5, we get:
H = 1.5/(1.5) = 1 inch
Therefore, the height of the rectangular prism is 1 inch.
Aren't you times 1.5 x 1.5 though?
You are correct. I made an error in the calculation.
Let's start over again.
Let the length of the rectangular prism be L, the width be W, and the height be H.
We know that the volume of the prism is 1.5 in.3:
V = LWH = 1.5
We are also given that the product of the length and width is 1.5 in.2:
LW = 1.5
Solving for one of the variables, let's say L:
L = 1.5/W
Substituting this into the equation for the volume:
V = LW * H = (1.5/W) * W * H = 1.5H
Therefore,
H = V/1.5 = 1.5/1.5 = 1 inch
So the height of the rectangular prism is 1 inch.
I apologize for the confusion!
To find the height of the prism, we need to use the formula for the volume of a rectangular prism.
The volume (V) of a rectangular prism is given by: V = length x width x height.
We are given that the volume is 1.5 in.3. Let's substitute this value into the formula: 1.5 = length x width x height.
We are also given that the product of the length and width is 1.5 in.2. Let's substitute this value as well: 1.5 = 1.5 x height.
Next, we need to isolate the height. Divide both sides of the equation by 1.5: height = 1.5 / 1.5.
Simplifying the expression, we get: height = 1.
Therefore, the height of the prism is 1 inch.