# The perimeter of an isosceles triangle ABC = 54 cm. AC is 4 times smaller than AB and BC.

September 29, 2021 | education

| **The perimeter of an isosceles triangle ABC = 54 cm. AC is 4 times smaller than AB and BC. Find the sides of a triangle ABC?**

An isosceles triangle is a triangle in which the two sides and the angles at these sides are equal, and the third side is called the base. Let’s denote the base, that is, the AC side behind x, then the AB side is equal to the BC side and is equal to 4x centimeters. Knowing that the perimeter is 54 centimeters. let’s make an equation. The perimeter of any shape is equal to the sum of the lengths of all its sides.

x + 4x + 4x = 54;

9 * x = 54;

x = 54/9;

x = 6 cm.

AC side = 6 cm, AB = BC = 6 * 4 = 24 centimeters.

Answer: 6 cm, 24 cm, 24 cm.

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