The perimeter of an equilateral triangle ABC is 24. PK is the middle line of the triangle.

The perimeter of an equilateral triangle ABC is 24. PK is the middle line of the triangle. Find the perimeter of the APKC quadrangle.

First, we find the length of each side of the triangle.
Recall that the perimeter is the sum of the lengths of all sides, which means that the perimeter of the triangle is:
P = a + b + c;
But triangle ABD is equilateral, so the formula will look like:
P = a + a + a = 3a
Find the sides of the triangle:
24: 3 = 8;
Secondly, let’s remember what the middle line of a triangle is.
The midline is a line segment parallel to the base and equal to half of it, connecting the midpoints of the two sides of the triangle.
Thus, AP and CK will be equal to half of the sides AB and BC, that is, 8: 2 = 4
PK will be equal to half the base, that is, 8: 2 = 4.
Find the perimeter of the APKC quadrangle:
8 + 4 + 4 + 4 = 20
Answer: 20