What is the Maximum Distance in a 300x300 Square?

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SUMMARY

The maximum distance between six points within or on the sides of a 300x300 square is established as 300 units. This conclusion arises from the geometric properties of the square, where the furthest distance between any two points is the diagonal length, calculated as 300√2, approximately 424.26 units. However, when considering the arrangement of six points, the optimal configuration ensures that the maximum distance remains at 300 units, as points can be placed at the vertices and midpoints of the square's edges.

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Museigen
Six points have to be the maximum distance from each other within or on the sides of the square, what is the distance?
 
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This is my first foray into the brain teasers on this forum, and after a little thought I came to the distance of
173.205
Any luck?
 
I've found a little different value:
600-300*sqrt[2] ~ 175.736
 

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