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
Answer by ankor@dixie-net.com(22740) (Show Source): 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>
:
Making a diagram of this will make easier to understand
:
Let x = Length of the longer side; (x-2) = width;
:
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
:
2(x^2 - 10x + 24) = 70
:
Simplify, divide equation by 2:
x^2 - 10x + 24 = 35
:
x^2 - 10x + 24 - 35
:
x^2 - 10x - 11 = 0
:
Factors to:
(x-11)(x+1) = 0
:
x = +11 has to be the solution
:
Dimensions of original rectangle: 11 by 9 units
:
Check using dimensions of box: 7 * 5 * 2 = 70
:
Could you follow this OK??
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