The perimeter of an isosceles triangle is 35 cm, and the base is 3 times the side. what is the length of the side?

An isosceles triangle has a base (c) and two equal sides (a = b).

The perimeter of a triangle (P) is equal to the sum of the lengths of all its sides:

P = a + b + c, since a = b, then P = 2a + c.

It is known from the condition of the problem that c = 3a.

Substitute the value c = 3a into the expression for the perimeter:

P = 2a + 3a = 5a.

Knowing the value of the perimeter of a given triangle, we calculate the length of its lateral side by the formula:

a = P: 5;

a = 35: 5;

a = 7.

We find that the length of the side of the given triangle is 7 cm.

Answer: 7 cm.