Answer: 6 inches should be used to create the appropriate box.
Explanation:
The volume (V) of a rectangular box is calculated as:
V = length x width x height
In this case, the width should be 2 more than the height, and the length should be 5 inches less than the height. So, we have:
Width (W) = Height (H) + 2
Length (L) = Height (H) - 5
The volume is given as 30 cubic inches so we can write the equation as:
30 = L x W x H
Substituting the expressions for width and length in terms of the height:
30 = (H - 5) x (H + 2) x H
Now, we can solve for the height (H):
30 = (H - 5)(H + 2)H
30 = (H^2 - 3H - 10)H
30 = H^3 - 3H^2 - 10H
Rearrange the equation:
H^3 - 3H^2 - 10H - 30 = 0
You can use a numerical method, like trial and error to find the value of H<3