Mathematics: 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?

54: 1, 2, 3, 6, 9, 18, 27, 5490: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90Step-by-step explanation:...

A map of a rectangular park has a length of 4 inches

kate9627

03.02.2022

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.

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