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

Algebra ->  Rectangles -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

x and y, the dimensions. Uncut cardboard.
xy=945.

Cutting off corners 3 by 3 square inches.
Base is %28x-2%2A3%29%28y-2%2A3%29
Height is simply 3.
VOLUME is 3%28x-6%29%28y-6%29=1755.
This volume equation can be a little bit more simplified initially:
Volume is %28x-6%29%28y-6%29=585.

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
xy-6x-6y%2B36=585
And substituting for xy=945 you get after a simplification,
-6x-6y%2B396=0
x%2By-66=0
Again substituting from the area as y=945%2Fx, obtain
after further steps,
.
highlight_green%28x%5E2-66x%2B945=0%29
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Using the general solution to a quadratic equation gives
x=%2866%2Bsqrt%28576%29%29%2F2
highlight%28x=45%29 (we use the positive square root).
From this and the area equation again, highlight%28y=21%29.