The perimeter of an isosceles triangle is 112 cm, and the base is 34 cm. Find one side.

Let x denote the length of the lateral side of this triangle.

In the initial data for this task, it is reported that this triangle is isosceles, therefore, the lengths of the sides of this triangle are equal and the length of the second side of this triangle should also be equal to x cm.

According to the condition of the problem, the sum of the lengths of all sides of this triangle is 112, and the length of the base is 34 cm, therefore, we can draw up the following equation:

x + x + 34 = 112,

solving which, we get:

2x + 34 = 112;

(2x + 34) / 2 = 112/2;

x + 17 = 56;

x = 56 – 17 = 39 cm.

Answer: 39 cm.