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

Question 188850This question is from textbook
: 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.
thanks This question is from textbook

Found 2 solutions by scott8148, ankor@dixie-net.com:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
let x=width, so x+2=length

the width of the box is x-2-2 or x-4
the length of the box is (x+2)-2-2 or x-2

the volume is 70
so 70 = 2 (x-2)(x-4)
dividing by 2 ___ 35 = x^2 - 6x + 8
subtracting 35 ___ 0 = x^2 -6x - 27
factoring ___ 0 = (x-9)(x+3)
x = 9 or x = -3

the original cardboard is 9in wide and 11in long
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.
:
Let x = the width of the cardboard
then
(x+2) = the length of the cardboard
:
4 units will be subtracted from the length and width
:
Length of the box: (x+2)-4 = (x-2)
Width of the box = (x-4)
Height of the box = 2 units
:
Find the area of the bottom of the box
(x-2)*(x-4) = x^2 - 6x + 8
:
Find the volume (Multiply by the height) given as 70 cu/units
2(x^2 - 6x + 8) = 70
:
Simplify, divide both sides by 2
x^2 - 6x + 8 = 35
:
A quadratic equation:
x^2 - 6x + 8 - 35 = 0
x^2 - 6x - 27 = 0
:
Factor this to
(x-9)(x+3) = 0
;
The positive solution is what we want here:
x = 9 units is the width of the cardboard
then
9 + 2 = 11 units is the length
;
:
Is this true?:
(9-4)(11-4) * 2 =
5 * 7 * 2 = 70 cu/units
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