the key for solving the above problem is knowing how to find the perimeter of a square inscribed inside a circle!
finding the circal circumference
circal r = 2
circumference whole circle 2*pi*r = 4*pi
finding 3/4 of circumference = 3/4*4*pi = 3*pi
draw a square inscribed inside a circle (look at the attachment)
the diagonal of the square is r=2*2=4 (diameter of circle).
the square forms two 45-45-90 triangles.
so the ratio is 1:1:sqrt(2) = 4/sqrt(2):4/sqrt(2):4
meaning the line in the attachment marked (1) equal 4/sqrt(2) and half the line is [4/sqrt(2)]/2
from the triangle with height 5 we can make two smaller right triangles with base [4/sqrt(2)]/2.
using the Pythagorean theorem will yield [[4/sqrt(2)]/2]^2+5^2=x^2
2+25 = x^2
x = sqrt(27)
so we can conclude that the sign circumference is pi*3+2*sqrt(27) or in other words pi*3+3*2sqrt(3) = pi*3+6sqrt(3)
and as was said before the answer is then (B)
untitled.GIF [ 2.33 KiB | Viewed 371 times ]