In the triangle midsegment theorem there are 2 parallel line

In the triangle midsegment theorem there are 2 parallel lines. The top one is one half times the bottom. If one of the lengths is labeled as a quadratic and you have to solve it, you get 2 answers. If they both work can there be two correct answers as the length? Also if you are finding the range of values for x in a triangle and it only gives you on side length and an angle measure, how do you find it?

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