Explanation:
Let's solve this problem step by step.
1. Start by drawing a diagram to visualize the problem. We have a square piece of sheet metal, and we need to remove squares from each corner to create an open box.
Let's assume the side length of the original square sheet metal is "x" feet.
After removing squares of side length 5 feet from each corner, the remaining dimensions of the sheet metal will be (x - 10) feet.
The height of the box will be 5 feet.
Therefore, the dimensions of the open box will be (x - 10) feet (length and width), 5 feet (height).
2. Use the formula for the volume of a rectangular box to set up an equation:
Volume = Length x Width x Height
Given that the volume is 720 cubic feet, we can write:
(x - 10) * (x - 10) * 5 = 720
Simplifying the equation:
5(x - 10)^2 = 720
3. Solve the equation to find the value of x:
Divide both sides of the equation by 5:
(x - 10)^2 = 144
Take the square root of both sides:
x - 10 = ±12
Solve for x:
x = 10 + 12 or x = 10 - 12
x = 22 or x = -2
Since we are dealing with lengths, we discard the negative value of x.
Therefore, the side length of the original square sheet metal is 22 feet.
4. Finally, calculate the dimensions of the sheet metal:
Length = Width = x - 10 = 22 - 10 = 12 feet
So, the dimensions of the sheet metal are 12 feet by 12 feet.
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