The bisector of an isosceles triangle reduced to its base is 12 cm. The side is 13 cm. Find the length of the base of the triangle.

In an isosceles triangle, the bisector drawn to the base is both the height and the median. So we have a right-angled triangle in which the lateral side is the hypotenuse, the bisector and half of the base are the legs. The sum of the squares of the legs is equal to the square of the hypotenuse. We denote half the length of the base of a given triangle by x. We can write the equation: 13 ^ 2 = 12 ^ 2 + x ^ 2; 169 = 144 + x ^ 2; x ^ 2 = 169-144 = 25; x = √25 = 5. If half of the base is 5 cm, then the total length of the base of the isosceles triangle given by the condition is 5 * 2 = 10 cm.