SOLUTION: The area of a rectangular piece of cardboard is 945 square inches. The cardboard is used to make an open box by cutting 3-inch squares from each corner and turning up the sides. If
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Question 849981: The area of a rectangular piece of cardboard is 945 square inches. The cardboard is used to make an open box by cutting 3-inch squares from each corner and turning up the sides. If the box is to have a volume of 1755 cubic inches, find the dimensions.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
x and y, the dimensions. Uncut cardboard.
.
Cutting off corners 3 by 3 square inches.
Base is
Height is simply 3.
VOLUME is .
This volume equation can be a little bit more simplified initially:
Volume is .
Let me leave this unfinished. The two equations to use are the system:
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xy=945
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(x-6)(y-6)=585
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The second equation, the volume one gives
And substituting for you get after a simplification,
Again substituting from the area as , obtain
after further steps,
.
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Using the general solution to a quadratic equation gives
(we use the positive square root).
From this and the area equation again, .
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