box with a square base is having a volume of 8 cubic meters. Let x be the length of the side of the square base and height of the box. What are the possible measurements of a side of the square base if the height should be longer than a side.

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2x

To find the possible measurements of the side of the square base, given that the height should be longer than a side, we can set up an inequality.

Let's start by assigning the variable x as the length of the side of the square base and also as the height of the box. We know that the volume (V) of the box is given by the formula:

V = length × width × height

Since we have a box with a square base, the length and width are the same, representing the side of the square base. Therefore, we can write the equation for the volume as:

8 = x × x × x

Simplifying this equation gives us:

8 = x^3

To solve for x, we need to find the cube root of both sides, giving us:

∛8 = ∛x^3

2 = x

So, x = 2.

Now, since the height should be longer than a side, we need to find the possible values of x that are greater than 2. Therefore, the possible measurements of a side of the square base are any values of x that are greater than 2.

In mathematical notation, we can express this as:

x > 2