SOLUTION: A piece of cardboard is 4cm longer than it is wide. From each corner a 2cm square is cut out and the cardboard is then folded to form an open box. What are the dimensions of the ca
Question 114148: A piece of cardboard is 4cm longer than it is wide. From each corner a 2cm square is cut out and the cardboard is then folded to form an open box. What are the dimensions of the cardboard if the box contains 64cm ^3 ? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A piece of cardboard is 4cm longer than it is wide. From each corner a 2cm square is cut out and the cardboard is then folded to form an open box. What are the dimensions of the cardboard if the box contains 64cm ^3 ?
:
Since we know the size of the squares that are cut out of the corners, we know that the height = 2 cm
Therefore we know that that base dimensions are 64/2 = 32
:
It becomes a simple matter of finding the dimensions of the base
:
Let x = the width
then
(x+4) = the length
:
x(x+4) = 32
:
x^2 + 4x = 32
:
x^2 + 4x - 32 = 0; a quadratic equation
:
Factors to:
(x+8)(x-4) = 0
:
The positive solution:
x = +4 is the width
then
4 + 4 = 8 is length
:
Check our solution by finding the volume: 8 * 4 * 2 = 64
