The height of an isosceles triangle = 12.4 cm, and the base is 40.6 cm, find the side of the triangle.

Since, by condition, the triangle is isosceles, then its height is also the median of the triangle, and therefore, it divides the base of the AC into equal segments AH and CH.

Then AH = CH = AC / 2 = 40.6 / 2 = 20.3 cm.

From the right-angled triangle ABN, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AH ^ 2 + BH ^ 2 = 20.3 ^ 2 + 12.4 ^ 2 = 412.09 + 153.76 = 565.85.

AB = √565.85 ≈ 23.79 cm.

Answer: The side of the triangle is 23.79 cm.