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? 7. jada wants to run a mile (5,280 feet). about how many times would she need to run around the park in order to reach her goal?

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 each side of the park is 10 cm on the map. Let the actual side - length be $s$. We set up a proportion $\frac{5}{200}=\frac{10}{s}$, cross - multiply to get $5s = 200\times10$, then $s=\frac{200\times10}{5}=400$ 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.

Step5: Calculate the number of times Jada needs to run around the park

If Jada wants to run 5280 feet and the perimeter of the park is 1600 feet, then the number of times $n$ is $n=\frac{5280}{1600}=3.3$ times.

Answer:

1. 12.5 cm
2. 1600 feet
3. 3.3 times