Answer:
Option B is correct.
The estimated perimeter of an ellipse is 37.3ft
Step-by-step explanation:
Given:
Length of Major-axis (2a)=15ft
Length of minor-axis (2b)=7.5ft
For an ellipse, the perimeter (P) approximately given by:
[tex]P\approx 2\pi\sqrt{\frac{a^2+b^2}{2}}[/tex] , where a and b are semi major axis and semi minor axis respectively.(Use approx. value of [tex]\pi =3.1 4[/tex])
Here, a=7.5ft and b=3.75ft, putting in above equation, we get
[tex]P\approx 2\pi\sqrt{\frac{\left (7.5\right )^2+\left (3.75\right )^2}{2}}[/tex]
[tex]P\approx 2\cdot 3.14\cdot \sqrt{\frac{56.25+14.0625}{2}}[/tex]
[tex]P\approx\ 6.28\cdot \sqrt{\frac{70.3125}{2}}[/tex]
[tex]P\approx\ 6.28\cdot \sqrt{35.15625}[/tex]
After solving the square-root we get,
[tex]P\approx\ 6.28\cdot5.92927061[/tex]
[tex]P\approx37.3ft[/tex].
Therefore, the estimated perimeter of an ellipse is 37.3ft.
