There is no reason whatsoever why the triangle should be rightangled.
What you need in order for the given side lengths to form a triangle is that the sum of the lengths of any two of the three sides should be greater than the length of the third side.
(So for example, side lengths 5, 6, 10 could form a triangle but 5, 6, 12 couldn't).
You have three inequalities.
(x + 11) + (2x + 10) > 5x - 9,
(x + 11) + (5x - 9) > 2x + 10,
(2x + 10) + (5x - 9) > x + 11.
Solving the first one,
3x + 21 > 5x - 9,
30 > 2x,
so x < 15.
Now solve the other two, and deduce a possible range of values for x.
-Bertie