## Task 2 - 230512

The measures of the (centimeter-measured) side lengths of a triangle are three consecutive natural numbers. The perimeter of this triangle is $42 \mathrm{~cm}$.

How long are its three sides?
The measure of the perimeter of a triangle is obtained by adding its three side lengths. Now, the sum of three consecutive natural numbers is equal to three times the middle of these three numbers (since the first number is one less and the third is one more than the middle number).

Since $42 \div 3 = 14$, the middle number in this case is 14, and the other two numbers are 13 and 15.

The sides of the triangle, whose perimeter is $42 \mathrm{~cm}$, are thus $13 \mathrm{~cm}, 14 \mathrm{~cm}$, and $15 \mathrm{~cm}$ long. These three side lengths also satisfy the condition that the sum of any two side lengths is always greater than the third side length.