Question

why can't a equilateral obtuse triangle exist

Answer 1

because the definition of equalateral is all sides the same. If all the angles are over 90 degrees it would over come the triangle limit of 180

Answer 2

even if we used the smallest obtuse angle
for example: the smallest obtuse angle is more than 90 degrees, so lets use 91 and since triangles have three sides...91+91+91=273
way over 180