Question

task b: paper towns
did you know that cartographers (people who create maps) used to create fake towns called \paper towns\ on their maps to detect when someone had copied their work?

1. make a scale drawing of the state of wyoming. the scale youre using is:
2. draw and label a paper town. make the location of the town be:
3. weston county resembles a square that is 45 miles by 45 miles. what is its approximate area on your map?

partner a: 3 centimeters to 90 miles, 135 miles from the southern edge of wyoming
partner b: 2 centimeters to 90 miles, 180 miles from the northern edge of wyoming

Explanation:

Step1: Calculate scale - factor for Partner A

For Partner A, the scale is 3 centimeters to 90 miles. The scale - factor is $\frac{3}{90}=\frac{1}{30}$ (centimeters per mile).

Step2: Calculate side - length of Weston County on the map for Partner A

The actual side - length of Weston County is 45 miles. Using the scale - factor, the side - length on the map $s_A = 45\times\frac{1}{30}=1.5$ centimeters.

Step3: Calculate area of Weston County on the map for Partner A

Since it's a square on the map, the area $A_A=s_A^2=(1.5)^2 = 2.25$ square centimeters.

Step4: Calculate scale - factor for Partner B

For Partner B, the scale is 2 centimeters to 90 miles. The scale - factor is $\frac{2}{90}=\frac{1}{45}$ (centimeters per mile).

Step5: Calculate side - length of Weston County on the map for Partner B

The actual side - length of Weston County is 45 miles. Using the scale - factor, the side - length on the map $s_B = 45\times\frac{1}{45}=1$ centimeter.

Step6: Calculate area of Weston County on the map for Partner B

Since it's a square on the map, the area $A_B=s_B^2=1^2 = 1$ square centimeter.

Answer:

Partner A: 2.25 square centimeters
Partner B: 1 square centimeter