Lots of Plots

Suppose there is a rectangular field of farmland that measures 140km × 252km. The land is going to be divided up into smaller square plots, each to grow a different type of produce. Your goal is to divide the land up into the largest possible square plots so that there is no land left over. Use the geogebra applet below to show what that would look like. You can type in the boxes that have numbers and you can drag the sliders to change your plot's length and width. When you are ready to see the plots of land, hit the show/hide plots button.

Let's start with our first rule, the plots have to be square. What does that mean for the length and width of our plots?

Check all that apply

Let's move to the second rule we must follow: There must be no left over land. What does that tell us about the length and width of our plot?

Check all that apply

Our final rule is that the squares need to be as large as possible. Taking what we learned from the two questions above, what does that mean about the value of the length and width of your plots?

Check all that apply

Sometimes your plot will be outlined in red and sometimes in green. Why is that?

What is the length of a side of the square plots?

How many square plots can you create?