To Find: The perimeter of the sixth inscribed equilateral triangle.

Given: Side of an equilateral triangle is 24 cm long.

As 2^nd triangle is formed by joining the midpoints of the sides of the first triangle whose side is equal to 24cm

[As shown in the figure]

So Side of a 2^nd equilateral triangle is 12 cm long [half of the first triangle side]

Side of 2^nd equilateral triangle = half of side of a 1^st equilateral triangle

Side of 3^rd equilateral triangle = half of side of a 2^nd equilateral triangle

…………. and So on

Therefore, Side of 6^th equilateral triangle = half of side of a 5^th equilateral triangle

So, Perimeter of a 6^th equilateral triangle is 3 times the side of a 6^th equilateral triangle

[NOTE: Perimeter of the triangle is equal to the sum of all three sides of the triangle, and in case of an equilateral triangle all sides are equal]

So,Perimeter of 6^th equilateral triangle = 30.75 = 2.25 cm