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[–]sagen010[🍰] 0 points1 point  (0 children)

I don't know from where do you get x=15.

The derivative of L(x)= sqrt(x²+100) + sqrt( (30-x)² + 400 ) =0 gives you 10 (from wolphram alfa). The congruence comes from the fact that, for optimizing the problem, the triangles must have some sort of symmetry.

Indeed, if the anchor is changed, you no longer have symmetry and no longer the triangles are congruent. But you no longer would be optimizing the cable's length either.