
Concept explainers
To calculate: The dimensions of the prism,
The volume of a rectangular prism is

Answer to Problem 2CYP
The value of length, width and height of a rectangular prism is:
Explanation of Solution
Given information:
The dimensions of the prism,
The volume of a rectangular prism is
Formula used:
For volume of a rectangle is,
Where:
Calculation:
Consider the statement as:
The volume of a rectangular prism is
The width of a prism is:
Then the length is
The height is
Recall that the area of the rectangle:
Apply the values in the formulas:
Simplified further:
Now to find the list of positive rational solutions for the expression look at the factors of the constants.
That are:
Here the last two terms subtracting values from the cube of the first and want to get zero,
So as have to take the positive number, and mostly take the less than mid-way.
So take a startup with
To get zero:
So the value is not zero its too grater than zero.
So check with the value
To get zero:
Here got the real root, it means
Now divide the expression
So the other factor is:
Now put the value in the formula:
Here the values of
To check the discriminants apply the values in the formula:
Its negative so can say that the other two roots are complex.
So, the real root is
Since the dimensions are:
That means:
Thus, the value of length, width and height of a rectangular prism is:
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