Answer:
the missing side of the prism is 144 units.
Explanation:
To find the missing side of the prism, we need to know the formula for the volume of a rectangular prism, which is:
V = l × w × h
where V is the volume, l is the length, w is the width, and h is the height of the prism.
If we know any three of these variables and the volume, we can solve for the fourth variable.
In this case, we are given the volume of the prism, which is 2688 cubic units. We are not given any of the dimensions directly. However, we can use the given information to set up an equation that relates the dimensions of the prism to its volume.
Let the missing side be x. Then, we have:
V = l × w × h
2688 = x × w × h
We don't know the values of w and h, but we can express their product as (w × h) and substitute this expression into the equation:
2688 = x × (w × h)
Now we need to factorize 2688 and see which pair of factors has a product that is also equal to (w × h).
One possible factorization is:
2688 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7
To simplify the calculations, we can pair up the factors as follows:
2688 = (2 × 2 × 2) × (2 × 3 × 3) × (2 × 2 × 7)
2688 = 8 × 18 × 28
So, we have:
x × (w × h) = 8 × 18 × 28
We know that x is one of the factors on the right-hand side. Since we want to find the value of x, we can divide both sides of the equation by (w × h):
x = (8 × 18 × 28)/(w × h)
We don't know the values of w and h, but we do know that they are both positive integers. Therefore, we can try different pairs of factors on the right-hand side of the equation until we find a pair that gives a positive integer value for x.
One possible pair of factors is 18 and 28:
x = (8 × 18 × 28)/(18 × 28) = 8 × 18 = 144
Therefore, the missing side of the prism is 144 units.