In an isosceles triangle, the lengths of the two sides are 6 cm and 12 cm. What is the length of the base of this triangle?

Since this triangle is isosceles, its two sides are equal.

According to the condition of the problem, the lengths of the two sides of this triangle are 6 cm and 12 cm.

Therefore, the base of this triangle can be 12 cm or 6 cm.

Let’s consider each of these cases.

1) The base of this triangle is 12 cm.

Then each of the lateral sides will be equal to 6 cm.

Since the sum of the lengths of the sides will be equal to the length of the base, such a triangle cannot exist.

2) The base of this triangle is 6 cm.

Then each of the lateral sides will be equal to 12 cm.

Since the sum of the lengths of any two sides of this triangle is greater than the length of its third side, then such a triangle exists.

Answer: 6 cm.