Answer :
Answer:
Step-by-step explanation:
Dimensions of the rectangular park = 4 inches by 6 inches
Since scale factor = [tex]\frac{\text{Dimensions of the park on map}}{\text{Dimensions of the original park}}[/tex] = [tex]\frac{1}{30}[/tex]
[tex]\frac{4}{\text{Length of the original park}}=\frac{1}{30}[/tex]
Length of the original park = 120 miles
Similarly, width of the park = 180 miles
Area of the park = Length × Width
= 120 × 180
= 21600 square miles
Therefore, area of the original park is 21600 square miles.
Formula for the ratio of area of the park on map and original park is,
[tex]\frac{\text{Area of the park on map}}{\text{Area of the original park}}=(\text{Scale factor})^2[/tex]
[tex]\frac{6}{21600}=(\text{Scale factor})^2[/tex]
Scale factor = [tex]\sqrt{\frac{1}{3600}}[/tex]
= [tex]\frac{1}{60}[/tex]
Scale factor to reproduce the map so that it fits in the brochure will be 1 inch for every 60 miles.