Triangle ABC is divided into equilateral triangles. The side of the filled triangle is 13 cm.

Triangle ABC is divided into equilateral triangles. The side of the filled triangle is 13 cm. find the perimeter of triangle ABC.

Let’s write down the formula for finding the perimeter of a triangle:

P = a + b + c.

However, in the presented problem, an equilateral triangle is given, which means that all sides will be equal to each other and its perimeter will be according to a slightly different formula:
P = 3a,

where a is the side of an equilateral triangle.

Let’s find the side of an equilateral triangle, since an equilateral triangle can only be divided into 4 smaller equilateral triangles (3 of which will be at the corners, and 1 in the center), then 1 side will be divided into half of 2 small triangles.

Therefore, to find the side ABC, you need to multiply the value of the sides of the small triangles by 2, since the side of the larger triangle divides 2 triangles:

13 cm * 2 = 16 cm – sides of triangle ABC.

We substitute in the formula for the perimeter of an equilateral triangle and get:

P = 3 * 16 cm = 48 cm.

Answer: 48 cm.