# The perimeter of the triangle is 120 cm, and the lengths of the sides are 2: 4: 6. Find the sides of the triangle.

June 25, 2021 | education

| In order to find the lengths of the sides of a triangle, we will compose and solve an equation.

Let’s look at the condition of the problem. We know that the perimeter of a triangle is 120 cm. It is also known that the lengths of the sides are in the ratio 2: 4: 6.

Let’s start by introducing a similarity coefficient k.

Then the sides of the triangle can be written as 2k; 4k and 6k.

We can now write the equation:

2k + 4k + 6k = 120;

k (2 + 4 + 6) = 120;

12k = 120;

k = 120: 12;

k = 10.

We found the coefficient of similarity. We find the lengths of the sides:

2 * 10 = 20 cm;

4 * 10 = 40 cm;

6 * 10 = 60 cm.

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