From the vertex B of the isosceles triangle ABC, a perpendicular BK equal to 12 cm was drawn to its plane

From the vertex B of the isosceles triangle ABC, a perpendicular BK equal to 12 cm was drawn to its plane. Find the distance from point K to the side AC, if AC = 24 cm, AB = BC = 20 cm.

In the isosceles triangle given by the condition, we draw the height (median) to the base of the speaker.
We find it by the Pythagorean theorem:
BH = √ (AB² – AH²) = √ (400 – 144) = √256 = 16 (cm).
The KBН triangle is rectangular. We find the hypotenuse KH – the distance from point K to the side of the AC.
KH = √ (BK² + BH²) = √ (144 + 256) = √400 = 20 (cm).
Answer: the distance from point K to the AC side is 20 cm.