Answer: [tex]24\ ft[/tex]
Step-by-step explanation:
The exercise gives you the following formula:
[tex]V = \frac{1}{3}hx^2[/tex]
Where "h" is the height of the square pyramid and "x" is the length of one side of the base.
According to the data given, you know that:
[tex]h=15\ ft\\\\V=2,880\ ft^3[/tex]
Therefore, you can subsitute these values into the formula:
[tex]2,880\ ft^3= \frac{1}{3}(15\ ft)x^2[/tex]
Now, you need to solve for the "x" to calculate the length of one side of the square base of that pyramid.
You get that this is:
[tex]2,880\ ft^3= \frac{1}{3}(15\ ft)x^2\\\\2,880\ ft^3= (\frac{15\ ft}{3})x^2\\\\2,880\ ft^3=(5\ ft)x^2\\\\\frac{2,880\ ft^3}{5\ ft}=x^2\\\\\sqrt{576\ ft^2}=x\\\\x=24\ ft[/tex]
