Question

Find an integer, x, such that 5, 10, and x represent the lengths of the sides of an obtuse triangle.

Answer 1

first, if it is a triangle then the interval for x is
(10-5) < x < 10+5
5 < x < 15

Answer 2

then the triangle above is an obtuse if satisfies :
5^2 + 10^2 < x^2
25 + 100 < x^2
125 < x^2

just check one by one for integer x in interval 5 < x < 15
for example x = 12
125 < 12^2
125 < 144
correct !