The ABC triangle is isosceles, ac = 5cm, ab = 8cm. which of these line segments is the base of the triangle?

As you know, an isosceles triangle is a triangle in which two sides are equal in length. Equal sides are called sides, and the third side is called the base. Let’s consider two possible cases. A) The base is a segment of the AC. B) The base is a segment AB.
A) The base is a segment of the AC. Then AC = 5 cm and AB = BS = 8 cm. Let us check the condition for the existence of a triangle with such side lengths. Generally speaking, there are several conditions for the existence of a triangle on three sides, for example, “Any triangle has the sum of any two sides greater than the third” or “Any triangle has a semiperimeter greater than any side.” Let’s apply the above second condition. Let p be the semiperimeter of the triangle ABC. Then p = (AB + AS + BS) / 2 = (8 cm + 5 cm + 8 cm) = (21 cm) / 2 = 10.5 cm. It is clear that p> AB, p> AC and p> BC … This means that a triangle with such sides has the right to exist, therefore, the AC segment can be the base of an isosceles triangle ABS.
B) Base – segment AB. Then AC = BC = 5 cm and AB = 8 cm. Let us check the condition for the existence of a triangle with such side lengths. The above second condition also applies here. Let p be the semiperimeter of the ABS triangle. Then p = (AB + AS + BS) / 2 = (8 cm + 5 cm + 5 cm) = (18 cm) / 2 = 9 cm. It is clear that p> AB, p> AC and p> BS. This means that a triangle with such sides also has the right to exist, therefore, the segment AB can also be the base of the isosceles triangle ABC.
Answer: The base of an isosceles triangle ABC with side lengths AC = 5 cm and AB = 8 cm can be either AC or AB.