Part B Ann’s second option is rezoning two separate plots of land. One is square, and the other is triangular with an area of 32,500 square meters. For this second option, the total area would be 76,600 square meters, which can be represented by this equation, where x is the side length of the square park: x2 + 32,500 = 76,600. Use the most direct method to solve this equation and find the side length of the square-shaped park. Explain your reasoning for both the solving process and the solution.

The side length of the square-shaped park is 120 meters.

Here we know that:

Here we Ann has two plots of land, one square and other triangular.

We know that the triangular one has an area of 32,500 m^2

And we also know that the total area is equal to 76,600 m^2

Then the area of the square plot will be equal to the difference between the total area and the area of the triangular plot.

area of the square plot = 76,600 m^2 - 32,500 m^2

Now, also remember that for a square of side length x, the area is given by:

A = x^2

Replacing that in the above equation we get:

x^2 = 76,600 m^2 - 32,500 m^2

Now we want to solve this for x, the side length of the square-shaped park.

First, let's solve the difference in the right side:

x^2 = 44,100 m^2

Now we can apply the square root in both sides to get:

√x^2 = √(44,100 m^2)

x = 210 m

The side length of the square-shaped park is 120 meters.

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