Find the length x in each triangle. Express your answer in simplified radical form.?

Question

The triangles length is 10, 8 , x

Answer 1

X can be any length greater than (10 - 8 = 2) and less than (10 + 8 = 18).

This is because no angle in the triangle is specified. In such a case, the minimum length of a third side is the greater than the absolute value of the difference between the other two sides and the maximum is less than the sum of the other two sides.

If it were exactly either value, the triangle would look like a few line segments piles together. Outside the range and not equal to either and the triangle is open (the sides do not join together).

Of course, one may choose assumptions and hope the test maker agrees they are good ones... If so, assuming it is a right triangle gives one the 6-8-10 triangle and the 8-10-2√41 triangle.

If you have other information, especially that the answer is desired in simplified radical form, it would seem the 8-10-2√41 triangle is the answer as it does have a simplified radical for an answer (2√41).

But all one can correctly state from the stated problem is 2 < X < 18.

Answer 2

The side is 6

6, 8, 10 is a right triangle, a multiple of the 3, 4, 5 right triangle.
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Answer 3

a^2 + b^2 = c^2, so let a =10, b=8, 100+64 = c^2, c=12.8

Answer 4

No availiable since I don't know the shape: give me a angle and the position of angle. Sorry . (Use law of cosines if you got an angle/ Right triangle?)