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Geometry of Triangles

The problem is not over yet:

The solution to the quadric is X = -6 or 4 which results in R = 65 (for X = -6) or 25 (for X = 4). The question now is "Which one is valid?" To find out you need to also solve for S and T using both values of X.

For X=-6, (R,S,T) = (65,220,-105)
For X=4, (R,S,T) = (25,80,75)

Since we do not live in a world with triangles with negative angles (-105), X must be 4 and therefore R = 25.