SOLUTION: A rectangular piece of cardboard is 2 units longer than it is wide. From each of its corners a square piece 2 units on a side is cut out. The flaps are then turned up to form an op
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Question 60956This question is from textbook Algebra For College Students
: A rectangular piece of cardboard is 2 units longer than it is wide. From each of its corners a square piece 2 units on a side is cut out. The flaps are then turned up to form an open box that has a volume of 70 cubic units. Find the length and width of the original piece of cardboard. This question is from textbook Algebra For College Students
You can put this solution on YOUR website! A rectangular piece of cardboard is 2 units longer than it is wide. From each of its corners a square piece 2 units on a side is cut out. The flaps are then turned up to form an open box that has a volume of 70 cubic units. Find the length and width of the original piece of cardboard>
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Making a diagram of this will make easier to understand
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Let x = Length of the longer side; (x-2) = width;
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After cutting out the square pieces which are the dimensions of the box:
(x-4) by (x-2)-4 by 2 so be can write the volume as: 2(x-4)(x-6) = 70
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2(x^2 - 10x + 24) = 70
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Simplify, divide equation by 2:
x^2 - 10x + 24 = 35
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x^2 - 10x + 24 - 35
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x^2 - 10x - 11 = 0
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Factors to:
(x-11)(x+1) = 0
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x = +11 has to be the solution
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Dimensions of original rectangle: 11 by 9 units
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Check using dimensions of box: 7 * 5 * 2 = 70
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Could you follow this OK??
