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?

Explanation:

Step1: Set up proportion for part a

Let $x$ be the actual length of the park. The scale is 1 inch to 300 feet, and the length on the map is 2 feet (24 inches). The proportion is $\frac{1}{300}=\frac{24}{x}$.

Step2: Cross - multiply and solve for $x$

$1\times x = 300\times24$. So $x = 7200$ feet.

Step3: Set up proportion for part b

Let $y$ be the length of the path on the map. The scale is 1 inch to 300 feet, and the actual length of the path is 750 feet. The proportion is $\frac{1}{300}=\frac{y}{750}$.

Step4: Cross - multiply and solve for $y$

$300y=750\times1$, then $y=\frac{750}{300}=2.5$ inches.

Answer:

a. 7200 feet
b. 2.5 inches