Question

In a regular hexagon with side 'n' another hexagon is drawn by joining the midpoints of the edges and so on. What will be the total perimeteeperimeter of all hexagons?

Answer 1

Answer:

soilved

Step-by-step explanation:

the original sid length = n

first   joining of  the midpoints of the edges side length = n√7/4

this process will make an infinite  G.P of lengths

n , n√7/4 , 7n/16 , ...

sum = n(1 ÷ 1 - √7/4) = 4n ÷ 4 - √7 = 4n/9( 4 + √7)

perimeter of all hexagons = (24n/9)×( 4 + √7) = (8/3)× ( 4 + √7)