In isosceles ABC, the base of the AC is three times smaller than its lateral side AB, and the perimeter is 28 cm.

In isosceles ABC, the base of the AC is three times smaller than its lateral side AB, and the perimeter is 28 cm. Find the lateral side of AB.

Let the length of the base of the triangle be X cm, AC = X cm, then, by condition, the length AB = 3 * X cm, and since the triangle is isosceles, then BC = AB = 3 * X cm.

Then the perimeter of the triangle is:

Ravs = AB + BC + AC = 3 * X + 3 * X + X = 7 * X cm.

7 * X = 27.

X = AC = 28/7 = 4 cm.

Then AB = 3 * 4 = 12 cm.

Answer: The length of the AB side is 12 cm.