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**n0083** I have two isosceles triangles that have the same base length, x.

For one of the isosceles triangles, the sides opposite the base angles have length sqrt(11).

For the other isosceles triangle, the sides opposite the base angles have length sqrt(17).

There is another triangle that has one side length x, one side length sqrt(11), and one side sqrt(17).

what is the value of x?

I do not see how to apply any law of sines/cosines without knowing an angle. I do not see how to apply any congruence theorems.

I suspect i am missing some theorem about isosceles triangles, perhaps?

Given two sides of a triangle, i ought to be able to find the third, no?

Thanks for your help.