We are given the following box
since the box is cubic, the height is the same as the length of the side length of its base.
The base would be a square of the following shape
where a is the length we are looking for. We are told that the area of the base is 49. Since the base has a side length of a, then we have the following equation
[tex]a^2=49[/tex]
By taking the square root on both sides, we get
[tex]a=\sqrt[]{49}=\pm7[/tex]
since a is a length, it should be positive. So, we have that
[tex]a=7[/tex]
then, the height of the box is 7 inches.
