Final answer:
Comparing lengths in mathematical problems involves using proportional reasoning, understanding the relationship between side lengths and areas of squares, and knowing the difference between displacement and total distance traveled in physics.
Step-by-step explanation:
The question pertains to comparing lengths and areas in a mathematical context, which is a typical topic in geometry. To address the question specifically, we use proportional reasoning and square area calculations.
For the scale length ratio, given that 1 inch represents 2000 miles, a scale length of 3 inches would represent x miles. The ratio would be set up as 1 inch / 2000 miles = 3 inches / x miles. By cross-multiplying, you can find the value of x to be 6000 miles.
In another example from geometry, Marta's squares show us that if one square has a side length that is twice as long as another, the area of the larger square will be four times the area of the smaller. This is because the area of a square is equal to the side length squared, and squaring the multiplier (2) gives us 4.
In physics, when discussing displacement, the distinction between total distance traveled and displacement is important. If xTotal is the total displacement, it is the sum of the individual displacements, XTotal = |Ax₁| + |Ax₂|, which is different from the path's total length traveled.