Answer:
The maximum dimensions of the box:
Length of the box = 0.788676 m
Breadth of the box = 0.288676 m
Step-by-step explanation:
Original piece of cardboard is a square with sides of length s.
Length of the card board = l = 1 m
Breadth of cardboard = b = 1/2 m = 0.5 m
Squares with sides of length x are cut out of each corner of a rectangular cardboard to form a box.
Now, length of the box = L = 1 - 2x
And breadth of the box = B = 0.5 - 2x
Height of the box ,H = x
Volume of the box ,V= L × B × H
x = 0.394338 , 0.105662
When , ,
(maxima)
The maximum dimensions of the box:
Length of the box = L = 1 - 2x = 1 - 2(0.105662) m = 0.788676 m
Breadth of the box = B = 0.5 - 2x = 0.5 - 2(0.105662) m = 0.288676 m