There is an equilateral triangle with each side of length 24 cm . The mid-point of its sides is join

Question

There is an equilateral triangle with each side of length 24 cm . The mid-point of its sides is joined to form another triangle. This process is going continuously infinitely many times. Then the sum of perimeter of first 6 triangles (in cm ) is

Professor PC Thomas Classes · Answer

Perimeters form a GP: $72, 36, 18 \dots$ Sum of first 6 terms $= \frac{72(1 - (1/2)^6)}{1 - 1/2} = 144(63/64) = 141.75$ cm.