Question

A park surveyor is drawing a scaled trail map of a park that is 180 acres long and 270 acres wide. On the map, if the park is 40 inches wide, how many inches long should it be?

Answer 1

To maintain the scale, if the width of the park on the map is 40 inches and the actual park is 270 acres wide and 180 acres long, the length on the map should be 26.67 inches.

Step-by-step explanation:

To find out how many inches long the park should be on the map, we need to use the scale between the actual size and the size on the map. Given that the park is 180 acres long and 270 acres wide, and the width on the map is 40 inches, we need to maintain the same ratio or proportion for the length on the map.

First, let's set up the proportion based on the given widths:

• Actual width : Map width = Actual length : Map length
• 270 acres : 40 inches = 180 acres : x inches

To solve for x (map length), we cross-multiply and divide:

(270 acres) * (x inches) = (40 inches) * (180 acres)

270x = 7200

x = 7200 / 270

x = 26.67 inches (rounded to two decimal places)

So, the map should be approximately 26.67 inches long to maintain the correct scale.