Long Rectangle Side of Cut Rectangle given all other Sides Calculator

Formula Used:

\[ S_{Long} = S_{Long\ Cut} + \sqrt{S_{Slant}^2 - (S_{Short} - S_{Short\ Cut})^2} \]

Long Cut Side of Cut Rectangle:

Slant Side of Cut Rectangle:

Short Rectangle Side of Cut Rectangle:

Short Cut Side of Cut Rectangle:

Long Rectangle Side of Cut Rectangle:

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1. What is the Long Rectangle Side of Cut Rectangle?

The Long Rectangle Side of Cut Rectangle is the length of the rectangle from which the Cut Rectangle shape forms. It represents the original full length before a portion was removed to create the cut rectangle shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ S_{Long} = S_{Long\ Cut} + \sqrt{S_{Slant}^2 - (S_{Short} - S_{Short\ Cut})^2} \]

Where:

\( S_{Long} \) — Long Rectangle Side of Cut Rectangle (m)
\( S_{Long\ Cut} \) — Long Cut Side of Cut Rectangle (m)
\( S_{Slant} \) — Slant Side of Cut Rectangle (m)
\( S_{Short} \) — Short Rectangle Side of Cut Rectangle (m)
\( S_{Short\ Cut} \) — Short Cut Side of Cut Rectangle (m)

3. Formula Explanation

Explanation: This formula calculates the original long side of a rectangle after a triangular portion has been cut from one corner. The formula uses the Pythagorean theorem to determine the missing segment length based on the slant side and the difference between the short sides.

Functions Used: sqrt - A square root function that takes a non-negative number as input and returns the square root of the given number.

4. Using the Calculator

Tips: Enter all values in meters. Ensure that the slant side is longer than the difference between the short rectangle side and short cut side to avoid negative square root values.

5. Frequently Asked Questions (FAQ)

Q1: What if I get a negative value under the square root?
A: This indicates invalid input. The slant side must be longer than the difference between the short rectangle side and short cut side for the geometry to be valid.

Q2: Can this calculator handle decimal values?
A: Yes, the calculator accepts and calculates with decimal values up to 4 decimal places precision.

Q3: What are typical applications of this calculation?
A: This calculation is useful in geometry, carpentry, construction, and any field dealing with cut rectangular shapes.

Q4: Are there any limitations to this formula?
A: The formula assumes a right-angled cut and may not apply to other types of cuts or non-rectangular shapes.

Q5: What units should I use?
A: The calculator uses meters, but you can use any consistent unit system as long as all inputs are in the same units.