In an isosceles triangle ABC, the side of AB is twice its base AC and the perimeter is 30cm. Find the speaker base.

Let x be the length AC of the base of this isosceles triangle ABC.

Let us express in terms of x the length of the lateral side AB of this triangle.

According to the condition of the problem, the lateral side of AB is twice as large as its base AC; therefore, the length of the lateral side AB is 2x.

Since this triangle is isosceles, the length of the second lateral side BC is also 2x.

According to the condition of the problem, the perimeter of this triangle is 30 cm, therefore, we can write:

x + 2x + 2x = 30.

We solve the resulting equation:

5x = 30;

x = 30/5;

x = 6 cm.

Answer: The length of the base of the speaker is 6 cm.