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 500 feet

Multiply the real - world distance by the scale factor. $500\times\frac{1}{40}=12.5$ cm.

Step3: Find the real - world side length of the park

Since the scale is 5 cm to 200 feet and the map side length is 10 cm. Let the real - world side length be $x$ feet. Set up a proportion $\frac{5}{200}=\frac{10}{x}$, cross - multiply gives $5x = 200\times10$, so $x = 400$ feet.

Step4: Calculate the perimeter of the park

The park is square, and the perimeter of a square is $P = 4s$. With $s = 400$ feet, $P=4\times400 = 1600$ feet.

Step5: Calculate the number of times around the park to run a mile

Divide the total distance of a mile (5280 feet) by the perimeter of the park. $\frac{5280}{1600}=3.3$ times.

Answer:

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