The formula to calculate the Short Edge of Parallelogram given Diagonals and Long Edge is:
\[ e_{\text{Short}} = \sqrt{\frac{d_{\text{Long}}^2 + d_{\text{Short}}^2 - (2 \cdot e_{\text{Long}}^2)}{2}} \]
The Short Edge of a Parallelogram is the length of the shortest pair of parallel edges in a Parallelogram. The Long Diagonal of a Parallelogram is the length of the line joining the pair of acute angle corners of a Parallelogram. The Short Diagonal of a Parallelogram is the length of the line joining the pair of obtuse angle corners of a Parallelogram. The Long Edge of a Parallelogram is the length of the longest pair of parallel sides in a Parallelogram.
Let's assume the following values:
Using the formula:
\[ e_{\text{Short}} = \sqrt{\frac{18^2 + 9^2 - (2 \cdot 12^2)}{2}} = 7.64852927038918 \]
The Short Edge of the Parallelogram is 7.64852927038918 meters.
| Long Diagonal (meters) | Short Diagonal (meters) | Long Edge (meters) | Short Edge (meters) |
|---|---|---|---|
| 16 | 9 | 12 | 4.949747468305833 |
| 16.5 | 9 | 12 | 5.711829829397931 |
| 17 | 9 | 12 | 6.403124237432849 |
| 17.5 | 9 | 12 | 7.044501401802686 |
| 18 | 9 | 12 | 7.648529270389178 |
| 18.5 | 9 | 12 | 8.223442101699263 |
| 19 | 9 | 12 | 8.774964387392123 |
| 19.5 | 9 | 12 | 9.307255234493143 |
| 20 | 9 | 12 | 9.823441352194250 |