Segment KA – perpendicular to the plane of the regular triangle ABC. Find the distance between the straight lines BC

Segment KA – perpendicular to the plane of the regular triangle ABC. Find the distance between the straight lines BC and SC if the perimeter of the triangle is 24cm.

According to the condition, the segment of the spacecraft is perpendicular to the plane of the triangle ABC, then the shortest distance from the AK to the side of the BC will be the perpendicular drawn from point A to the side of BC. Since the triangle ABC is correct, the height coincides with the median, which means BH = CH = BC / 2.
In a regular triangle, all sides are equal, then Ravs = 3 * AB.
AB = BC = СD = 24/3 = 8 cm.
BH = CH = 8/2 = 4 cm.
From the right-angled triangle AHC, we define the leg AH according to the Pythagorean theorem.
AH^2 = AC^2 – CH^2 = 64 – 16 = 48.
AH = √48 = 4 * √3 cm.
Answer: The distance between the straight lines BC and KA is 4 * √3 cm.