Question

You work for a real estate development company that is trying to determine the perimeter of a lake. The company is planning to split up the land around the lake into different properties. As you examine the lake, you notice that a particular oddity manifests. From an aerial view, the lake shore looks smooth like a curve. However, as you zoom in and take a closer look you notice that the lake shore has ridges and nooks. If you walk around the lake, you see that the ridges and nooks have smaller ridges and nooks of their own . Formulate a discussion that addresses this issue and propose a method that would best approximate the perimeter of the lake.

Answer 1

Answer:

Answer explained below.

Step-by-step explanation:

It is important for the real estate company to precisely measure the perimeter of the lake. The company proposes to split up the land around the lake into different properties. For maximizing profits it becomes crucial for the company to get as close to the exact perimeter around the lake as possible so that selling of properties around the lake becomes more feasible and helps in inculcating profits.

Earlier from the aerial view it was obtained that the lake shore looks like a smooth curve and perimeter estimation could have been very easy for such a surface. However, closer view into the shore shows that the shore has some nooks and ridges. Now this oddity around the lake can actually lead to under estimation of the lake shore using conventional methods of perimeter estimation. These ridges and nooks further have smaller ridges and nooks. This can further add to the perimeter as well as real estate profit. So it will be in the favor of the company to estimate the perimeter around the lake by not using the conventional estimation method of calculation of perimeter of a curve , but take into account these oddities and add them to the perimeter as well.

For the purpose of the estimation the best method will be to measure the entire lake shore with a rope which can mimic the shape of the shore given its oddities. However, considering the size of the lake and the amount of manual labor that will get into this exercise one has to resort to other methods such as, dividing the shore in parts where the perimeter seems to be smooth. Within these parts sub parts can be divided for further ridges and nooks. For each sub part the perimeter can be estimated using the conventional methods. The last step will be to add all the sub part to obtain the perimeter of the part and then add all the parts to get the perimeter of the entire lake shore.

Further, these ridges can nooks can also serve as a demarcation for the plots that need to be sold by the real estate company.