Thread: Equilateral Triangle

How long is the largest equialteral trangle that can be inscribed in a square with side length of 1?
I had intially thought 1, but others told me I was wrong.

Hello, ceasar_19134!

How long is the largest equialteral trangle
that can be inscribed in a square with side length of 1?

The triangle can be inscribed like this . . .

Code:

      *-----------------*
      |*    *           |
      | *         *     |
      |  *              *
    1 |   * x         * |
      |    *        *   |
      |     * 60° *     |
      |  75° *  * 45°   |
      *-------*---------*

Let x = side of the equilateral triangle.

In the lower-left right triangle, we have; .sin75° = 1/x

Hence: .x .= .1/sin75° .= .1.03527615