In an isosceles triangle ABC, base AC = 16 cm, height 6 cm, find the side.

1. Let us denote by the symbol H the point of intersection of the height drawn from the vertex B with the base of the AC.

2. Proceeding from the fact that in an isosceles triangle, the height BH is the median dividing the base of the AC into two equal parts, we calculate the length of the segment AH:

AH = CH = 16: 2 = 8 centimeters.

3. Applying the Pythagorean theorem, we calculate the length of the lateral side AB of the triangle ABC:

AB = √BH ^ 2 + AH ^ 2 = √36 + 64 = √100 = 10 centimeters.

Answer: the length of the lateral side AB of triangle ABC is 10 centimeters.