Find the perimeter of an equilateral triangle if it is 26 cm larger than its side.

The perimeter of a triangle is the sum of the lengths of all its sides.

Since in an equilateral triangle all sides are equal, then its perimeter is:

P = a + a + a = 3a, where a is the length of each side of the triangle.

From the condition of the problem it is known that the perimeter of an equilateral triangle is 26 cm larger than its side, which means that the following expression can be written:

3a – a = 26.

Let’s solve this equation:

2a = 26;

a = 26: 2;

a = 13.

We find that the side of an equilateral triangle is 13 cm.

Let’s calculate its perimeter:

P = 3 * 13 = 39 cm.

Answer: 39 cm.