If you draw it you can see that
An = An-1 * .25
or
a , .25 a , .25^2 a etc
we have a sum of a geometric series here with r = .25
see
http://www.mathsisfun.com/algebra/sequences-sums-geometric.html
the first term a is area of triangle with 8 x sides
a = 2 * 4x * 4x sqrt 3
= 32 sqrt 3
sun of infinite geometric series
= a /(1-r)
= 32 sqrt 3 /.75
= 42.67 sqrt 3
The large red equilateral triangle has sides of 8x units. The midpoints of the red triangle are joined to form the blue triangle. The midpoints of the blue triangle ate joined to form the green triangle. The process of joining midpoints to form new triangles continues indefinitely
Urgent##1. Solve for x if the sum of all the areas is given by 19200 square root 3
2 answers
so A total = 32 x^2 sqrt 3/.75
so
32 x^2 sqrt 3/.75 = 19200 sqrt 3
x^2 = 450
x = 21.2
check my arithmetic
so
32 x^2 sqrt 3/.75 = 19200 sqrt 3
x^2 = 450
x = 21.2
check my arithmetic