Answer:
Option B is correct.
The estimated perimeter of an ellipse is 37.3ft
Step-by-step explanation:
<u>Given:</u>
Length of Major-axis (2a)=15ft
Length of minor-axis (2b)=7.5ft
For an ellipse, the perimeter (P) approximately given by:
, where a and b are semi major axis and semi minor axis respectively.(Use approx. value of
)
Here, a=7.5ft and b=3.75ft, putting in above equation, we get
![P\approx 2\pi\sqrt{\frac{\left (7.5\right )^2+\left (3.75\right )^2}{2}}](https://tex.z-dn.net/?f=P%5Capprox%202%5Cpi%5Csqrt%7B%5Cfrac%7B%5Cleft%20%287.5%5Cright%20%29%5E2%2B%5Cleft%20%283.75%5Cright%20%29%5E2%7D%7B2%7D%7D)
![P\approx 2\cdot 3.14\cdot \sqrt{\frac{56.25+14.0625}{2}}](https://tex.z-dn.net/?f=P%5Capprox%202%5Ccdot%203.14%5Ccdot%20%5Csqrt%7B%5Cfrac%7B56.25%2B14.0625%7D%7B2%7D%7D)
![P\approx\ 6.28\cdot \sqrt{\frac{70.3125}{2}}](https://tex.z-dn.net/?f=P%5Capprox%5C%206.28%5Ccdot%20%5Csqrt%7B%5Cfrac%7B70.3125%7D%7B2%7D%7D)
![P\approx\ 6.28\cdot \sqrt{35.15625}](https://tex.z-dn.net/?f=P%5Capprox%5C%206.28%5Ccdot%20%5Csqrt%7B35.15625%7D)
After solving the square-root we get,
![P\approx\ 6.28\cdot5.92927061](https://tex.z-dn.net/?f=P%5Capprox%5C%206.28%5Ccdot5.92927061)
.
Therefore, the estimated perimeter of an ellipse is 37.3ft.