The sides of a triangle are expressed in simple two-digit numbers. Find the smallest value for the perimeter of this triangle.

Consider simple two-digit numbers, starting with the smallest: 11, 13, 17, 19, 23, and so on.

These numbers will express the length of the sides of the triangle if the triangle inequality holds for them. Let’s check the first three:

11 + 13> 17;

11 + 17> 13;

13 + 17> 11.

We see that for the numbers 11, 13 and 17, the triangle inequality holds, which means that they can act as the lengths of its sides. Find the perimeter as the sum of the three sides of the triangle:

P = 11 + 13 + 17 = 41.

Answer: 41.