Toby is making a model of a battlefield. The actual area is 11 miles by 7.5 miles. He wants to put the model on a 3.25 ft by 3.25 ft square table with at least 3 inches on each side between the model and table edges. What is the largest scale he can use?
To find the largest scale Toby can use for the model, we need to calculate the dimensions of the model based on the given table size and the required empty space around the model.
First, let's convert the dimensions of the actual area from miles to feet:
Length of actual area: 11 miles * 5280 ft/mile = 58080 ft
Width of actual area: 7.5 miles * 5280 ft/mile = 39600 ft
Considering that Toby wants at least 3 inches (or 0.25 ft) of empty space on each side between the model and the table edges, we need to subtract this from the dimensions of the table:
Length of table area available for the model: 3.25 ft - (2 * 0.25 ft) = 2.75 ft
Width of table area available for the model: 3.25 ft - (2 * 0.25 ft) = 2.75 ft
Now, we can calculate the scale by dividing the dimensions of the actual area by the dimensions of the table area available for the model:
Scale = (Length of actual area) / (Length of table area available for the model) = 58080 ft / 2.75 ft ≈ 21,083.64
Scale = (Width of actual area) / (Width of table area available for the model) = 39600 ft / 2.75 ft ≈ 14,400
Therefore, the largest scale Toby can use is around 21,083:1 or 14,400:1.