Drawing a triangle within a square/rectangle

• Jul 19th 2011, 09:32 AM
triplell
Drawing a triangle within a square/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?

I know that I can find all the angles of using the Law of Cosines. After all this I end up with rectangle with 4 triangles inside of it.

I feel like I should be able to solve this problem.
• Jul 19th 2011, 10:15 AM
waqarhaider
Re: Drawing a triangle within a square/rectangle
what is the relation between sides of triangle and rectangle
• Jul 19th 2011, 11:01 AM
triplell
Re: Drawing a triangle within a square/rectangle
No sides of the triangle share the same sides as the rectangle, so there are 4 separate triangles all together.

I know that it would be possible if one of the sides of the triangle was also the side of the rectangle, producing only three separate triangles.

The more I wrack my head around this, the more I think it's not possible.
• Jul 19th 2011, 12:01 PM
Soroban
Re: Drawing a triangle within a square/rectangle
Hello, triplell!

There is no unique rectangle.

Quote:

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.