SOLUTION: An open box is to be constructed from a rectangular sheet of metal by removing a one-foot by one-foot square from each corner and turning up the edges. The length of the sheet of
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Question 71469This question is from textbook College Algebra
: An open box is to be constructed from a rectangular sheet of metal by removing a one-foot by one-foot square from each corner and turning up the edges. The length of the sheet of metal is twice the width. If the box is to hold 4 cubic feet. What should be the dimensions of the sheet metal? This question is from textbook College Algebra
You can put this solution on YOUR website! An open box is to be constructed from a rectangular sheet of metal by removing a one-foot by one-foot square from each corner and turning up the edges. The length of the sheet of metal is twice the width. If the box is to hold 4 cubic feet. What should be the dimensions of the sheet metal?
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It would help to draw out this as described. A rectangle:
Let x = width
Then 2x = length
:
Cut out the 1 ft squares from each corner and you can see that the dimensions of the box will be: (x-2) by (2x-2) by 1 ft
:
A simple volume equation, width * length * ht = 4
(x-2)(2x-2)(1) = 400
FOIL
2x^2 - 2x - 4x + 4 = 4
2x^2 - 6x + 4 = 4
2x^2 - 6x + 4 - 4 = 0
2x^2 - 6x = 0
Factor
2x(x - 3)= 0
x = + 3 ft, is the solution we want
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The metal rectangle is 3 by 6 ft
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The box (3-2) by (6 - 2), a 1 by 4 by 1 ft box
:
Check using 1*4*1 = 4 cu ft
