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

August 25, 2021 | education

| A triangle is three points that do not lie on one straight line, connected by segments. In this case, the points are called the vertices of the triangle, and the segments are called its sides.

An isosceles triangle is a triangle in which the sides are equal.

AB = BC.

The perimeter of a triangle is the sum of all its sides:

P = AB + BC + AC.

Since the ratio of the base of the AC and the sides of AB and BC is 2: 3, and the perimeter of the triangle is 56 cm, then we express:

2x – the length of the base of the speaker;

3x – the length of the sides AB and BC;

2x + 3x + 3x = 56;

8x = 56;

x = 56/8 = 7;

AC = 2 ∙ 7 = 14 cm;

AB = BC = 3.7 = 21 cm.

Answer: the length of the base of the AC is 14 cm, the length of the sides AB and BC is 21 cm.

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