Final answer:
The original width of the piece of metal is 25 inches and the original length is 30 inches.
Step-by-step explanation:
To find the original dimensions of the piece of metal, we need to find the length and width before the squares were cut. Let's let the width be x inches. According to the problem, the length is 5 inches longer than the width, so the length would be x+5 inches.
After the squares with sides 1 inch long are cut from the corners, the dimensions of the resulting box would be (x-2) inches (length), (x-2) inches (width), and 1 inch (height). The volume of the box would be (x-2)(x-2)(1) = 594 cubic inches.
Simplifying this equation and solving for x, we have (x-2)(x-2) = 594. Expanding and rearranging, we get x^2-4x+4 = 594. Subtracting 594 from both sides, we have x^2-4x-590 = 0. Using the quadratic formula, we find that x = 25 or x = -23. Since the width cannot be negative, the original width of the piece of metal is 25 inches.
To find the original length, we can substitute the value of x = 25 into the equation for the length, which is x+5. Therefore, the original length of the piece of metal is 25+5 = 30 inches.