The perimeter of a triangle is 54 cm. Find its sides if they are 2: 3.

From the condition it is known that the perimeter of a triangle is 54 cm. And it is also known that its sides are related as 2: 3: 4. In order to find the lengths of the sides of the triangle, we compose and solve the equation.

So, let’s start by introducing the similarity coefficient k. Then we can write the lengths of the sides of the triangle as:

2k; 3k and 4k.

Formula for calculating the perimeter of a triangle:

P = a + b + c;

2k + 3k + 4k = 54;

We solve the equation:

9k = 54;

k = 6.

So, the sides of the triangle are equal: 2 * 6 = 12 cm; 3 * 6 = 18 cm; 4 * 6 = 24 cm.