Answer:
The minimum length of the shoreline is 100.26 km
Step-by-step explanation:
We can start by assuming that the shape of the lake can be approximated to be a circle.
We need to understand that the length of the shoreline that we are looking for is the circumference of the circle.
From the area of the circle, we can get the radius as follows:
[tex]Area = \pi r^{2}\\r = \sqrt{\frac{Area}{\pi}} \\r = \sqrt{\frac{800}{\pi}}= 15.96 km[/tex]
The circumference of the circle can be got using the formula
[tex]circumference = 2\pi r[/tex]
[tex]circumference = 2 \times \pi \times 15.96=100.26 km[/tex]
Therefore, the minimum length of the shoreline is 100.26 km
