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.

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- October 1st 2006, 12:45 PMceasar_19134Equilateral 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. - October 1st 2006, 02:07 PMSoroban
Hello, ceasar_19134!

Quote:

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