Question

a wildlife park is in the shape of a rectangle. a map of the wildlife park is made with the scale 1 inch to 300 feet.
a. if the wildlife park is shown as a rectangle on the map with a length of 2 feet, what is the actual length of the park?
b. if a straight path in the park is 750 feet long, how long would the path be when represented on the map?

1. what is the scale factor from the larger figure to the smaller figure?

is figure b a scaled copy/dilation of figure a? why? explain your answer.
a) no
b) yes

Explanation:

Step1: Convert map - length to inches for part a

Since 1 foot = 12 inches, 2 feet on the map is $2\times12 = 24$ inches.

Step2: Calculate actual length for part a

The scale is 1 inch to 300 feet. So the actual length is $24\times300=7200$ feet.

Step3: Calculate map - length for part b

Let the length on the map be $x$ inches. Using the scale $\frac{1}{300}=\frac{x}{750}$. Cross - multiply gives $300x = 750$, then $x=\frac{750}{300}=2.5$ inches.

Answer:

a. 7200 feet
b. 2.5 inches