Problema Solution
A rectangular cardboard sheet has a length that is 1.5 times greater than the width. Is it possible to make a topless box with a volume of 6080 cm3 out of this cardboard sheet if squares with a side of 8 cm are cut from the corners? Find the dimensions of the cardboard sheet.
Answer provided by our tutors
Let
x = the width of the cardboard sheet
1.5x = the length of the cardboard sheet
y = 8 cm length of the sides of the removed squares.
Then the dimensions of the box will be: (1.5x-2y) by (x-2y) by y.
The volume of the box is 6080 cm^3, therefore:
(1.5x-2y)*(x-2y)*y = 6080
Since y = 8 cm we have:
(1.5x-2*8)*(x-2*8)*8 = 6080
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click here to see the equation solved for x
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x = 36 cm
We need to ignore the negative solution since the width is always positive.
1.5x = 1.5*36 = 54 cm
The dimensions of the rectangular cardboard sheet are 56 cm by 36 cm.