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There seems to be a similar question in this exchange:

How could I use the centroid and size of a triangle to find the coordinates of its vertices?

But this one specifies that it has the centroid and the size of the triangle.

In my case what i am trying to do is to calculate the minimum bounding box for a triangle but i only have the following information:

  • X, Y coordinates of the center of the triangle
  • Length of the each sides.

Can anyone give me a hint? or this is also not possible.

Thx!

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    You can find the minimum area, of the box, but not the coordinates of the box. – 2017-02-21
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    Imagine a long thin triangle rotating around its centroid. What happens to the bounding box? – 2017-02-21
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    Well the bounding box might change yes, but I know that The bounding box of a Triangle is going to be a Rectangle with the smallest and largest x,y from any point. – 2017-02-21
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    So do you want the minmal box that would fit all triangles with the given constraints? – 2017-02-21
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    I basically need all 3 X,Y coordinates that actually form the triangle. Is there such a possiblity that if i do follow cosine law, i can find the angles. so assume i also have the angles somehow – 2017-02-21
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    you can't find them because they are not well defined. You can rotate the triangle around its centroid. – 2017-02-21
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    @emirozer You cannot have unique such coordinates because you can always rotate the triangle – 2017-02-21
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    + reflection (permutation of sides) – 2017-02-21
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    What you can do is find a bounding box (a square, actually) such that the vertices are guaranteed to be inside or on the boundary of the bounding box regardless of how the triangle is rotated, and there is no smaller bounding box with that property. – 2017-02-21
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    Is someone here learning Erlang? – 2017-02-23

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The triangle is only determined up to rotations and reflections.

Let $G$ be the centroid of $\triangle ABC$. The length of the medians can be calculated in terms of the sides using the median length formula. That gives the length of $GA$ as $2/3$ the length of the median through $A$. Choose $A$ to be any point on the circle centered at $G$ of radius $GA$. Now construct $B$ knowing the distances $AB,GB\,$, then $C$ the same way. Depending on the choice of $B$ on either side of $GA$ this gives two possible triangles $ABC$ which are reflections of each other.