SOLUTION: A rectangular piece of cardboard is twice as long as it is wide. A 4-cm square is cut out of each corner, and the sides are turned up to make a box with an open top. The volume of
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Question 805870: A rectangular piece of cardboard is twice as long as it is wide. A 4-cm square is cut out of each corner, and the sides are turned up to make a box with an open top. The volume of the box is 616 cm3. Find the original dimensions of the cardboard.
This is what I have so far....
4 cm x 2x=616cm^3
would i them subtract 4 cm from both sides I am stuck and don't really know where to go from here.
You can put this solution on YOUR website! A rectangular piece of cardboard is twice as long as it is wide.
A 4-cm square is cut out of each corner, and the sides are turned up to make a box with an open top.
The volume of the box is 616 cm3.
Find the original dimensions of the cardboard.
:
removing the 4 cm squares will reduce the dimensions by 8 cm
4cm will be the height of the box
:
L = 2w
The volume equation
(2w-8)*(w-8)*4 = 616
simplify, divide both sides by 4
(2w-8)*(w-8) = 154
FOIL
2w^2 - 16w - 8w + 64 = 154
2w^2 - 24w + 64 - 154 = 0
A quadratic equation
2w^2 - 24w - 90 = 0
simplify divide by 2
w^2 - 12w - 45 = 0
Factors to
(w-15)(w+3) = 0
The positive solution is all we want here
w = 15 cm is the width of the cardboard
then
2(15) = 30 cm is the length
:
:
:
You can confirm this by replacing w in the vol equation
(2w-8)*(w-8)*4 = 616
