Find the base and side of an isosceles triangle if its two sides are 5 cm and 11 cm.

It follows from the triangle inequality that the length of any side of a triangle is less than the sum of its two other sides.
Let a, b and c be the sides of the triangle, then:
a + b> c;
a + c> b;
b + c> a.
1. The sides of an isosceles triangle a and b are 5 cm each, and the base is 11 cm then:
5 + 5> 11;
5 + 11> 5;
5 + 11> 5.
Since 5 + 5 <11, then an isosceles triangle with a side equal to 5 cm and a base equal to 11 cm does not exist.
2. The sides of an isosceles triangle a and b are 11 cm each, and the base is 5 cm then:
11 + 11> 5;
11 + 5> 11;
11 + 5> 11.
All inequalities are satisfied, then an isosceles triangle with a side equal to 11 cm and a base equal to 5 cm exists.
Answer: base = 5 cm, side = 11 cm.