A rectangular piece of copper is 6 inches longer than it is wide....

mauricev

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A rectangular piece of copper is 6 inches longer than it is wide. To make a tray, a one-inch square is cut out of each corner and then the sides are folded up. The resulting tray is one inch deep and the base has an area of 160 square inches. What are the dimensions of the original piece of copper?

This led me to the equation (w-2)(w+4) = 160, but this leads to a quadratic that isn't factorable and I tend to doubt that was the intention. Is this equation correct?
 

Dr.Peterson

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A rectangular piece of copper is 6 inches longer than it is wide. To make a tray, a one-inch square is cut out of each corner and then the sides are folded up. The resulting tray is one inch deep and the base has an area of 160 square inches. What are the dimensions of the original piece of copper?

This led me to the equation (w-2)(w+4) = 160, but this leads to a quadratic that isn't factorable and I tend to doubt that was the intention. Is this equation correct?
Actually it is factorable. What convinced you that it is not?

But why does it have to be factorable? You can always solve the equation by the quadratic formula (unless you haven't learned it yet); you wouldn't get nice integer dimensions, but that happens only when a teacher is being nice to you -- not in the real world!
 

mauricev

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Actually it is factorable. What convinced you that it is not?

But why does it have to be factorable? You can always solve the equation by the quadratic formula (unless you haven't learned it yet); you wouldn't get nice integer dimensions, but that happens only when a teacher is being nice to you -- not in the real world!
You're right. MathPapa led me to believe--erroneously--it wasn't.
 

Dr.Peterson

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You're right. MathPapa led me to believe--erroneously--it wasn't.
I hadn't heard of the site, perhaps for good reasons.

Note that if you think a quadratic trinomial might not be factorable, you can check by calculating the discriminant. If it is a perfect square, then the trinomial is factorable; then you can either factor it, or continue with the quadratic formula.
 

mauricev

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