The lateral side of an isosceles triangle is twice the base and 12 cm less than the perimeter

The lateral side of an isosceles triangle is twice the base and 12 cm less than the perimeter of the triangle. Find the base of the triangle.

Based on the condition of the problem and the above properties of an isosceles triangle, we introduce into the problem the variable x (cm) – the base of the triangle, then (2 * x) cm – each side of the triangle. The perimeter of a triangle (P) is the sum of all its sides. By hypothesis, we have (2 * x) = (P – 12), therefore, P = (2 * x + 12) cm. Means:
P = 2 * x + 2 * x + x (perimeter is the sum of all sides);
P = 5 * x, where P = (2 * x + 12);
2 * x + 12 = 5 * x;
-3 * x = -12;
x = 4 (cm) – the required base of the triangle.
Answer: The base of the triangle is 4 cm.