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?
3.25 feet = 39 inches
39 - 6 = 33 inches
11/33 = 3 inches for 1 mile
Multiply 11 by 7.5 which is 82.5. Next multiply 3.25 by 3.25. Now multiply 12 by 1056.25.
To determine the largest scale Toby can use for his model, we need to find the scale factor that will fit the actual area onto the given table size.
Here's how to calculate it:
1. Find the dimensions of the table: Since the table is a square with sides measuring 3.25 ft, the area of the table is (3.25 ft) * (3.25 ft) = 10.5625 square feet.
2. Find the required area between the model and table edges: Toby wants at least 3 inches (0.25 ft) on each side between the model and the table edges. So, the required area is (0.25 ft + 11 miles + 0.25 ft) * (0.25 ft + 7.5 miles + 0.25 ft) = 11.5 miles * 7.75 miles.
3. Calculate the scale factor: Divide the required area by the table area to find the scale factor: (11.5 miles * 7.75 miles) / 10.5625 square feet.
To simplify the calculation, we can convert the miles to feet:
- 1 mile = 5280 feet
- 11.5 miles = 11.5 * 5280 feet
- 7.75 miles = 7.75 * 5280 feet
So, the scale factor is ((11.5 * 5280) feet * (7.75 * 5280) feet) / 10.5625 square feet.
Calculating this will give us the largest scale Toby can use for his model.