The sides of a triangle are 2: 3: 4. The smaller side of a similar triangle is 4 cm. What is the perimeter of the second triangle?

Similar triangles are triangles in which the corresponding sides are proportional.

Let us assume that the sides of the first triangle are equal: AB = 2 cm, BC = 3 cm, AC = 4 cm.Since the length of the smaller side of the A1B1C1 triangle is 4 cm, we can find the coefficient of similarity:

k = A1B1 / AB;

k = 4/2 = 2.

Now we can find the remaining unknown sides:

В1С1 = ВС · k;

В1С1 = 3 2 = 6 cm;

A1C1 = AC · k;

A1C1 = 4 2 = 8 cm.

Now we can find the perimeter:

P = A1B1 + B1C1 + A1C1;

P = 4 + 6 + 8 = 18 cm.

Answer: the perimeter of triangle A1B1C1 is 18 cm.