SOLUTION: a rectangular piece of cardboard has an area of 15cm2. By cutting a square 2cm wide on each side from each of the corners and fold up the sides an open box is formed having a volu

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Question 766489: a rectangular piece of cardboard has an area of 15cm2. By cutting a square 2cm wide on each side from each of the corners and fold up the sides an open box is formed having a volume of 132ml.find the lenght of the original cardboard?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This rectangular board is x by y cm^2, and both lengths are variable.
The area allows us xy=15 cm^2. Equivalently, y=15%2Fx

Cutting out the corners and folding to make the rectangular space you have height of 2 cm, so 2%28x-2%2A2%29%28y-2%2A2%29=132,
simplifiable to
%28x-4%29%28y-4%29=66
And we earlier found a formula for y relating to x using the initial carboard area....

%28x-4%29%2815%2Fx-4%29=66
x%2A15%2Fx-4x-4%2A15%2Fx%2B16=66
15-4x-60%2Fx%2B16=66
-4x-60%2Fx=66-31
-4x-60%2Fx=35
-4x%5E2-60=35x
-4x%5E2-35x-60=0
highlight%282x%5E2%2B17.5x%2B30=0%29
highlight%284x%5E2%2B35x%2B60=0%29

General solution to quadratic equation:
x=%28-35%2B-sqrt%2835%5E2-4%2A4%2A60%29%29%2F%282%2A4%29
x=%28-35%2B-sqrt%28265%29%29%2F8
We want the positive value for x:
...It's not happening...
....?


CONSIDER:
Taking out a 2 by 2 square at each corner means 4*(2*2) cm^2 removed. This is 16 cm^2, but you were only given 15 cm^2. The problem is therefore impossible.