Question

problems 5 - 7: jada is looking at a map of a square park that has a scale of 5 centimeters to 200 feet. on the map, each side of the park is 10 centimeters long. 5. jada lives 500 feet from the park. how long would this distance be on the map? 6. if jada ran around the perimeter of the park once, what distance would she run?

Explanation:

Step1: Find the scale factor

The scale is 5 cm to 200 feet, so the scale - factor is $\frac{5}{200}=\frac{1}{40}$ (cm per foot).

Step2: Calculate the map - distance for Jada's home

If Jada lives 500 feet from the park, then the map - distance $d$ is $d = 500\times\frac{1}{40}=12.5$ cm.

Step3: Find the actual side - length of the park

Since 5 cm on the map represents 200 feet and the side of the park on the map is 10 cm. Let the actual side - length of the park be $s$. We set up a proportion: $\frac{5}{200}=\frac{10}{s}$, cross - multiply gives $5s = 200\times10$, so $s = 400$ feet.

Step4: Calculate the perimeter of the park

The park is square, and the perimeter $P$ of a square with side - length $s$ is $P = 4s$. Substituting $s = 400$ feet, we get $P=4\times400 = 1600$ feet.

Answer:

1. 12.5 cm
2. 1600 feet