To find the length of the tin rectangle, we need to set up and solve an equation based on the given information.
Let's start by visualizing the rectangular sheet of tin before any cuts are made:
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The width of the tin rectangle is given as 3 meters (since it is 3 meters wide).
Now, we are instructed to cut out a 1-meter square from each corner:
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After making these cuts, we can fold up the sides to form an open box:
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____1____ ____1____
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Now, we are told that the volume of the box should be 2 cubic meters. The volume of a rectangular box is given by the formula length × width × height.
In this case, since the box is open at the top, the height is the same as the length of the cut-out squares. Hence, the height of the box is 1 meter.
Let's denote the length of the tin rectangle as L. After folding up the sides, the resulting length of the box will be L - 2 (since we removed two 1-meter squares).
Therefore, the volume of the box is (L - 2) × 3 × 1 = 2.
Now, we can set up and solve the equation:
(L - 2) × 3 = 2
First, let's distribute the 3:
3L - 6 = 2
Next, let's isolate L:
3L = 2 + 6
3L = 8
Dividing both sides by 3:
L = 8/3
So, the length of the tin rectangle is 8/3 meters, or approximately 2.67 meters.