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The formula calculates the length of a cuboid when its space diagonal, width, and height are known. It is derived from the Pythagorean theorem applied in three dimensions.
The calculator uses the formula:
Where:
Explanation: The formula applies the three-dimensional Pythagorean theorem to find the length component when the space diagonal and the other two dimensions are known.
Details: Calculating the length of a cuboid from its space diagonal is important in geometry, architecture, engineering, and various practical applications where complete dimensional information is needed but only partial measurements are available.
Tips: Enter the space diagonal, width, and height in meters. All values must be positive numbers. The space diagonal must be greater than the square root of the sum of squares of width and height for a valid result.
Q1: What is a space diagonal in a cuboid?
A: The space diagonal is the longest straight line that can be drawn from one vertex of the cuboid to the opposite vertex, passing through the interior of the cuboid.
Q2: Can this formula be used for any rectangular prism?
A: Yes, since a cuboid is a type of rectangular prism, this formula applies to all rectangular prisms.
Q3: What if the calculated length is imaginary?
A: An imaginary result indicates that the input values are inconsistent - the space diagonal must be at least as long as the diagonal of the face formed by width and height.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input measurements. The accuracy of the result depends on the accuracy of the input values.
Q5: Can this formula be rearranged to find other dimensions?
A: Yes, the formula can be rearranged to find width or height if the other dimensions and space diagonal are known.