The perimeters of such triangles are 2: 5, and the sum of their large sides

The perimeters of such triangles are 2: 5, and the sum of their large sides is 56 cm.Find the sides of a triangle if the sides of one of them are 2: 3: 4

In such triangles, the corresponding sides are proportional as well as their perimeters. Since we know the proportion of their perimeters, we find the large sides by making an equation, where:

2x – large side of a small triangle;

5x – large side of the large triangle;

2x + 5x = 56 cm;

7x = 56;

x = 56/7;

x = 8;

2x = 2 * 8 = 16 cm;

5x = 5 * 8 = 40 cm;

The large sides of such triangles are 16 cm and 40 cm;

Since the sides of each triangle are in the ratio 2: 3: 4, we express through x – one part of this proportion, then:

4x = 16 cm (large side) for a small triangle;

x = 4;

Then the sides of the small triangle are equal = 2x, 3x, 4x = 6 cm, 12 cm, 16 cm;

4x = 40 cm (large side) for a large triangle;

x = 10;

Then the sides of the large triangle are = 2x, 3x, 4x = 20 cm, 30 cm, 40 cm.