Yes
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No. Due to Pythagoras' Theorem, the square of the hypotenuse (the longest side of the right triangle) has to be equal to the sum of the squares of the other two sides. If this is too wordy, call the sides a, b and c, where c is the hypotenuse. Then a2+b2=c2 for any right triangle. Hence, with 3, 6 and 8 we have 9+36=64 (or 36+9=64 depending on how you choose a and b) which is clearly wrong, so a triangle with sides of length 3, 6 and 8 is NOT a right triangle.
36. If the length of the line segment joining the midpoints of two sides of an equilateral triangle is 6 the perimeter of the triangle is 36.
Only a right triangle has a hypotenuse. An isosceles triangle can be a right triangle but it doesn't have to be. If it's not, then it doesn't have a hypotenuse.
Using Pythagoras' theorem the length of the hypotenuse is 39 units of measurement.