Answer:
The answer is below
Step-by-step explanation:
The volume of box = width * length * height
120 = x * x * y
120 = x²y
y=120/x²
The surface area (SA) = sum of the area of all faces side
SA = x² + x² + xy + xy + xy + xy
SA = 2x² + 4xy
substitute y =120/x²
SA = 2x² + 4x(120/x²)
SA = 2x² + 480/x
Taking the derivative:
SA' = 4x - 480/x²
making SA' = 0:
0 = 4x - 480/x²
480/x² = 4x
4x³ = 480
x³ = 120
x = 4.93 feet
y = 120 / x² = 120 / 4.93² = 4.93
Hence the width, length and height is 4.93 feet.
