SOLUTION: Four squares, each with sides 4 cm long, are cut from the corners of a rectangular piece of cardboard having an area 560 cm^2. The flaps are then bent up to form an open topped bo
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Question 299905: Four squares, each with sides 4 cm long, are cut from the corners of a rectangular piece of cardboard having an area 560 cm^2. The flaps are then bent up to form an open topped box having volume 960 cm^3. Find the dimensions of the original piece of cardboard.
Thank you! Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website! xy=560 or x=560/y
(x-8)(y-8)*4=960
(560/y-8)(y-8)*4=960 divide both sides by 4.
(560-8y-4480/y+64)=240
(-8y-4480/y)=240-64-560
-8y-4480/y=-384
(-8y*y-4480)/y=-384 cross multiply.
-8y^2-4480=-384y
-8y^2+384y=4480
8y^2-384y+4480=0
8(y^2-48y+560)=0
8(y-28)(y-20)=0
y-28=0
y=28 x=560/28=20 ans.
y-20=0
y=20 x=560/20=28 ans.
Proof:
(28-8)(20-8)*4=960
20*12*4=960
960=960
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