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

July 28, 2021 | education

| Given:

isosceles triangle ABC,

P ABC = 56 centimeters,

AB and BC – lateral sides,

АС – bases,

AC: AB = 2: 3.

Find the lengths of the sides of the triangle ABC, that is, AB, BC, AC -?

Solution:

Let the length of the AC side be 2 * x centimeters, then the lengths of the AB and BC sides are 3 * x centimeters. We know that the perimeter of this isosceles triangle is 56 centimeters. Let’s make the equation:

2 * x + 3 * x + 3 * x = 56;

x * (2 + 3 + 3) = 56;

x * 8 = 56 (in order to find an unknown factor, you need to divide the product by a known factor);

x = 56: 8;

x = 7 centimeters;

7 * 2 = 14 centimeters – the length of the speaker side;

3 * 7 = 21 centimeters – the lengths of the sides AB and BC.

Answer: 14 centimeters; 21 centimeters; 21 centimeters.

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