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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