Either the new side or 10 has to be the hypotenuse of a triangle.
Case one ======= The hypotenuse is 10 10^2 = 8^2 + b^2 b^2 = 36 b = 6 so the new side has to be more than 6 but less than 10.
Case two ======= The new side is the hypotenuse of a right triangle 8^2 + 10^2 = 64 + 100 = 164 sqrt(164) = 12.8 So the new side has to be less than 12.8 but greater than 6
Answer The second one <<<< =========== 6 < s < 12.8
