Given ABC – isosceles triangle. Side AB = BC = 10 cm. BO – triangle height = 6 cm. Find the base of this triangle.

Since the triangle, by condition, is isosceles, AB = BC, then the height of the BH of the triangle is also the median of the triangle, and therefore AH = CH.

Consider a right-angled triangle ABN, in which the angle H = 900, since BH is the height of the triangle.

Then, by the Pythagorean theorem, AH ^ 2 = AB ^ 2 – BH ^ 2.

AH ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64.

AH = 8 cm.

Since AH = CH, then AC = 2 * AH = 2 * 8 = 16 cm.

Answer: The base of the triangle is 16 cm.