Hello, triplell!

There is no unique rectangle.

Let's say I have a rectangle shape.

Inside that shape, I draw a triangle.

I know the length of all the sides of that triangle.

Is it possible to find out the length of the rectangle?

No sides of the triangle share the same sides as the rectangle,

so there are *four* separate triangles all together.

From your description, one vertex of the triangle is a vertex of the rectangle.

Code:

*-------*-------*
| .*::* |
| .*:::::* |
|.*::::::::* |
*:::::::::::* |
| *::::::::* |
| *:::::* |
| *::*|
*---------------*

The triangle can be rotated slightly

and another rectangle can be circumscribed around it.

Code:

*--------*----*
| .*:::. |
| .*::::::* |
*::::::::::. |
| *::::::::* |
| *:::::::. |
| *:::::* |
| *::::.|
| *::*|
| *:|
*-------------*

There are an infinite number of such rectangles.