Answer:
x = 3.53 ft
y - 3.53 ft
z = 3.53 ft
Step-by-step explanation:
given details
volume = 44 ft^3
let cardboard dimension is x and y and height be z
we know that area of given cardboard without lid is given as
A = xy + 2xy + 2yz
xyz = 44 ft^3
To minimize area we have
A = xy + 2x (44/xy) + 2y(44/xy)
A = xy + (44/y) + (44/x)
we have
................1
..............2
from 1 and 2
xy(y-x) = 0
xy = 0 or y = x
from geometry of probelem
x ≠ 0 and y ≠ 0
so y = x
x^3 = 44
x = 3.53 ft = y
z = 44/xy = 3.53