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
Answer by ankor@dixie-net.com(22740)   (Show Source):
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?
:
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
:
The metal rectangle is 3 by 6 ft
:
The box (3-2) by (6 - 2), a 1 by 4 by 1 ft box
:
Check using 1*4*1 = 4 cu ft
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