Final answer:
To find the length of rope required to tie the ends of an elliptical garden, we can use the formula for the circumference of an ellipse. By plugging in the values of the semi-major and semi-minor axes, we can calculate the length of rope needed. In this case, the length of rope required is approximately 17.77 meters.
Step-by-step explanation:
To find the length of the rope required to tie the ends of an elliptical garden, we need to know the formula to calculate the circumference of an ellipse. The formula is given by: C = 2π * sqrt((a^2 + b^2)/2) where a is the semi-major axis and b is the semi-minor axis. In this case, the width of the ellipse is the semi-major axis, so a = 8/2 = 4 meters.
Now we can calculate the semi-minor axis b by using the formula: b = a * sqrt(1 - e^2) where e is the eccentricity. For a circular ellipse, e = 0, so b is equal to the semi-major axis, which in this case is 4 meters.
Plugging the values of a and b into the formula for the circumference, we get C = 2π * sqrt((4^2 + 4^2)/2) = 2π * sqrt(16 + 16)/2 = 2π * sqrt(32)/2 = π * sqrt(32) = 4π * sqrt(2) ≈ 17.77 meters.