Solve the problem. An open box is to be made from a rectangular piece of tin by cutting two inch squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin.

More information is needed to come up with a unique set of Length/Width dimensions. The area of the base must be 50 square inches, since the side height of the box is 2 inches.

(L-2)(W-2) = 50

The smallest rectangle that will do the job is a square, with L = W.

To solve this problem, we need to follow a few steps:

Step 1: Understand the problem.
We have a rectangular piece of tin and we need to cut two-inch squares out of the corners. Then, we'll fold up the remaining sides to form an open box. The volume of the box is given as 100 cubic inches. We need to find the dimensions of the rectangular piece of tin.

Step 2: Define the variables.
Let's assign variables to the dimensions of the tin:
- Length of the tin: L (in inches)
- Width of the tin: W (in inches)

Step 3: Identify the constraints and relationships.
Given that we need to cut 2-inch squares out of the corners, the dimensions of the open box will be reduced by 4 inches (2 inches on each side) from the original dimensions of the tin.

The height of the box is not explicitly mentioned but is defined by the folded-up sides. We'll call the height of the box H (in inches).

The relationship between the dimensions is as follows:
Length of the box (after folding) = L - 4 inches
Width of the box (after folding) = W - 4 inches
Height of the box = H inches

The volume of the box can be calculated using the formula:
Volume = Length × Width × Height

Step 4: Set up the equation.
Given that the volume of the box is 100 cubic inches, we can set up the equation as follows:
100 = (L - 4) * (W - 4) * H

Step 5: Solve the equation.
To solve this equation, we need more information. We can either assume the value of one of the variables or look for additional information in the problem statement.

Let's assume a value for H:
Let H = 2 inches

Substituting this value into the equation, we get:
100 = (L - 4) * (W - 4) * 2

Step 6: Simplify and solve for the dimensions.
Divide both sides of the equation by 2:
50 = (L - 4) * (W - 4)

Now, we need to find two factors of 50 that differ by 4 since (L - 4) * (W - 4) = 50.

The factors of 50 are:
1, 2, 5, 10, 25, 50

After trying different values, we find that L - 4 = 10 and W - 4 = 5 satisfy the equation. Adding 4 to both sides, we get:
L = 14 inches and W = 9 inches

Step 7: Check the solution.
Now that we have the values of L and W, we can calculate the height (H) and verify if the volume of the box is indeed 100 cubic inches.

Using the formula Volume = Length × Width × Height, we substitute the values:
Volume = 14 * 9 * 2 = 252 cubic inches

Since the volume is not equal to 100 cubic inches, our assumption for the height (H) was incorrect.

To find the correct value for the height, we divide 100 by the product of (L - 4) and (W - 4):
H = 100 / ((L - 4) * (W - 4)) = 100 / ((14 - 4) * (9 - 4)) = 100 / (10 * 5) = 2 inches (correct value)

So, the dimensions of the rectangular piece of tin are:
Length (L) = 14 inches
Width (W) = 9 inches
Height (H) = 2 inches