Toby is making a scale model of the battlefield at Fredericksburg. The area he wants to model measures about 11 mi by 7.5mi. He plans to put the model on a 3.25 ft by 3.25ft square table. On each side of the model he wants to leave at least 3 inches between the model and the table edges. What is the largest scale he can use? I need help!!!
i d k but if youre in math course 7th grade im in too and u don't answer if u don't kno it cuzz this is one of the challenege questions teacher just mark as extra credit if u want but it really doesnt count
11 miles by 7.5 miles is the size of a town. I don't think he plans to build something that large
To determine the largest scale Toby can use for his model, we need to calculate the maximum length that can fit on one side of the table while leaving at least 3 inches of space between the model and the table edge.
First, convert the dimensions of the area to be modeled into feet to match the table dimensions. We can use the conversion factor 1 mile = 5280 feet.
Length of the modeled area = 11 mi * 5280 ft/mi = 58080 ft
Width of the modeled area = 7.5 mi * 5280 ft/mi = 39600 ft
Next, subtract the space Toby wants to leave on each side of the model from the corresponding dimension of the table.
Length of the table (minus empty space) = 3.25 ft - 2 * 3 inches = 3.25 ft - 2 * (3/12) ft = 3.25 ft - 1/6 ft = 3 ft + 1/2 ft = 3.5 ft
Width of the table (minus empty space) = 3.25 ft - 2 * 3 inches = 3.25 ft - 2 * (3/12) ft = 3.25 ft - 1/6 ft = 3 ft + 1/12 ft = 3.08 ft
Now, we can find the maximum scale Toby can use by dividing the length or width of the modeled area by the corresponding dimension of the table (minus empty space).
Maximum scale = Length of the modeled area / Length of the table (minus empty space)
= 58080 ft / 3.5 ft
≈ 16608
Similarly,
Maximum scale = Width of the modeled area / Width of the table (minus empty space)
= 39600 ft / 3.08 ft
≈ 12863
Therefore, the largest scale Toby can use is approximately 16608:1 or 12863:1, depending on whether he prioritizes the length or width of the area to be modeled.