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

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}}` =
`(1)/(30)`

`\frac{4}{\text{Length of the original park}}=(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`

`(6)/(21600)=(\text{Scale factor})^2`

Scale factor =
`\sqrt{(1)/(3600)}`

=
`(1)/(60)`

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