In an isosceles triangle ABC with a perimeter of 56 cm, the base refers to the lateral side as 2: 3.

In an isosceles triangle ABC with a perimeter of 56 cm, the base refers to the lateral side as 2: 3. find the sides of the triangle

Since, by condition, the triangle ABC is isosceles, then AB = BC.

Let the side AB = BC = 2 * X cm, then, by the condition AC = 3 * X.

Since the perimeter of the triangle is 56 cm, then AB + BC + AC = 56 cm.

2 * X + 2 * X + 3 * X = 56.

7 * X = 56.

X = 56/7 = 8.

Then AB = BC = 2 * 8 = 16 cm.

AC = 3 * 8 = 24 cm.

Answer: The sides of the triangle are 16 cm, 16 cm and 24 cm.