Given – ABC-isosceles triangle perimeter = 56cm AC: BC = 2: 3 find AC BC AB.

Let the length of the base of the AC equal to 2 * X cm, then the side of the BC, by condition, is equal to 3 * X cm.

Since the condition does not indicate which sides in the triangle are equal, consider two options.

Let AB = BC = 3 * X.

Then the perimeter of the triangle will be equal to: P = AB + BC + AC = 3 * X + 3 * X + 2 * X = 8 * X = 56 cm.

X = 56/8 = 7 cm.

Then AB = BC = 3 * 7 = 21 cm.

AC = 2 * 7 = 14 cm.

Let AB = AC = 2 * X.

Then the perimeter of the triangle will be equal to: P = AB + BC + AC = 2 * X + 3 * X + 2 * X = 7 * X = 56 cm.

X = 56/7 = 8 cm.

Then BC = 3 * 8 = 24 cm.

AC = AB = 2 * 8 = 16 cm.

Answer: The sides of the triangle are 14 cm, 21 cm, 21 cm, or 24 cm, 16 cm, 16 cm.