In triangular ABC, side AB is 2 times larger than side BC and 3cm less than side AC.

In triangular ABC, side AB is 2 times larger than side BC and 3cm less than side AC. Find the length of the side of the AC if the perimeter of the triangle ABC is 23cm.

Let the length of the AC side be x centimeters, then by condition the length of the AB side is (x – 3) centimeters.

Let us find the length of the side BC if it is known that it is half the length of the side AB:

((x – 3): 2 = 0.5 * x – 1.5) cm.

Considering that the perimeter of this triangle, that is, the sum of the lengths of its sides is 23 centimeters, we compose and solve the equation:

x + (x – 3) + (0.5 * x – 1.5) = 23;

x + x – 3 + 0.5 * x – 1.5 = 23;

2.5 * x = 27.5;

x = 27.5 / 2.5;

x = 11.

Answer: The length of the speaker side is 11 centimeters.