Question

A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 Miles. What is the actual area of the park? The map needs to be reproduced at a different scale so that it has an area of 6 square inches and can fit in a brochure. At what scale should the map be reproduced so that it fits on the brochure?

Answer 1

Answer:

Step-by-step explanation:

Dimensions of the rectangular park = 4 inches by 6 inches

Since scale factor = $\frac{\text{Dimensions of the park on map}}{\text{Dimensions of the original park}}$ = $\frac{1}{30}$

$\frac{4}{\text{Length of the original park}}=\frac{1}{30}$

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,

$\frac{\text{Area of the park on map}}{\text{Area of the original park}}=(\text{Scale factor})^2$

$\frac{6}{21600}=(\text{Scale factor})^2$

Scale factor = $\sqrt{\frac{1}{3600}}$

                    = $\frac{1}{60}$

Scale factor to reproduce the map so that it fits in the brochure will be 1 inch for every 60 miles.