Answer:
Length and width of the box = 3.05 feet
Height of the box = 6.12 feet
Step-by-step explanation:
Let the side of square base of the rectangular box is x feet and height is h feet.
therefore volume of the box V = x² × h-----------(1)
It has been given that George has a material to create the box with an area = 56 square feet
Box consists one base + one cover + four sides
So area of a rectangular box with square base = 2×(area of base) + 4×(area of one side) = 56 square feet
2(x)²+ 4(xh) = 56
2(x² + 2xh) = 56
x² + xh = 28
xh = 28 - x²
-------(2)
Now we put the value of h in equation (1)
![V=[\frac{28-x^{2}}{x}]x^{2}=x(28-x^{2})](https://tex.z-dn.net/?f=V%3D%5B%5Cfrac%7B28-x%5E%7B2%7D%7D%7Bx%7D%5Dx%5E%7B2%7D%3Dx%2828-x%5E%7B2%7D%29)
To find the maximum volume we will find the derivative of volume and then equate it to zero.
V=28x - x³

3x² = 28

Now we put the value of x in equation 2

Therefore length and width of the box are 3.05 feet and height is 6.12 feet