The formula to calculate the Diagonal of a Rectangle given Perimeter and Length is:
\[ d = \sqrt{(2l^2) - (Pl) + \left(\frac{P^2}{4}\right)} \]
Where:
The Diagonal of a Rectangle is the length of the line joining any pair of opposite vertices of the Rectangle.
Length of Rectangle is any one of the pair of parallel sides which are longer than the remaining pair of parallel sides.
Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.
Let's assume the following values:
Using the formula:
\[ d = \sqrt{(2 \cdot 8^2) - (28 \cdot 8) + \left(\frac{28^2}{4}\right)} \]
Evaluating:
\[ d = \sqrt{(2 \cdot 8^2) - (28 \cdot 8) + \left(\frac{28^2}{4}\right)} \]
The Diagonal of the Rectangle is 10 Meter.
| Length of Rectangle (Meter) | Perimeter of Rectangle (Meter) | Diagonal of Rectangle (Meter) |
|---|---|---|
| 6 | 24 | 8.485281374238570 |
| 6 | 26 | 9.219544457292887 |
| 6 | 28 | 10.000000000000000 |
| 6 | 30 | 10.816653826391969 |
| 6 | 32 | 11.661903789690601 |
| 7 | 24 | 8.602325267042627 |
| 7 | 26 | 9.219544457292887 |
| 7 | 28 | 9.899494936611665 |
| 7 | 30 | 10.630145812734650 |
| 7 | 32 | 11.401754250991379 |
| 8 | 24 | 8.944271909999159 |
| 8 | 26 | 9.433981132056603 |
| 8 | 28 | 10.000000000000000 |
| 8 | 30 | 10.630145812734650 |
| 8 | 32 | 11.313708498984761 |
| 9 | 24 | 9.486832980505138 |
| 9 | 26 | 9.848857801796104 |
| 9 | 28 | 10.295630140987001 |
| 9 | 30 | 10.816653826391969 |
| 9 | 32 | 11.401754250991379 |
| 10 | 24 | 10.198039027185569 |
| 10 | 26 | 10.440306508910551 |
| 10 | 28 | 10.770329614269007 |
| 10 | 30 | 11.180339887498949 |
| 10 | 32 | 11.661903789690601 |