The median drawn to one of the equal side of an isosceles triangle divides its perimeter into two parts 15 cm and 6 cm in length. Find the length of the base of the triangle.

In an isosceles triangle, the median to an equal side divides perimeter into 15 and 6. Let equal sides = a, base = x, median to one equal side splits that side. Two cases: median to base splits triangle differently. For base x: perimeter parts are (a + median segment) and (a - median segment + x). Testing x=1: equal sides become 8.5, perimeter parts are 6 and 15. For x=10: triangle inequality fails. Answer is 1 cm.