Question 2

Explanation

Our goal is to find the area of each plot in three locations (A, B, and C) with the condition that the number of plots in each location must be the same and maximized.

Since the number of plots must be the same and maximized, we need to find the Greatest Common Divisor (GCD) of the land areas: $120$, $180$, and $240$. This GCD value will represent the number of plots to be created.

Let's perform prime factorization for the three numbers:

The GCD is obtained by multiplying the common prime factors with the lowest exponent:

• Factor 2: the lowest exponent is $2^2$.
• Factor 3: the lowest exponent is $3^1$ (or 3).
• Factor 5: the lowest exponent is $5^1$ (or 5).

So, the number of plots to be created in each location is 60 plots.

Next, we calculate the area of each plot for each location by dividing the total land area by the number of plots ($60$):

Location A:

Location B:

Location C:

Thus, the area of each plot from each location respectively is $2\text{ m}^2$, $3\text{ m}^2$, and $4\text{ m}^2$.