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? 8) here is a scale drawing of lafayette square in washington, d.c. if the scale is 1 inch to 200 feet, determine the actual dimensions of lafayette square. lafayette square 2.5 in. 4 in.

Explanation:

Step1: Find map - to - real ratio

The scale is 5 centimeters to 200 feet, so the ratio is $\frac{5}{200}=\frac{1}{40}$ (1 centimeter on map represents 40 feet in real - life).

Step2: Calculate map distance for Jada's home

Jada lives 500 feet from the park. Let $x$ be the map distance. Using the ratio $\frac{1}{40}=\frac{x}{500}$, we can cross - multiply: $40x = 500$, then $x=\frac{500}{40}=12.5$ centimeters.

Step3: Find actual side - length of the park

Since 5 centimeters on the map represents 200 feet and the side of the park on the map is 10 centimeters. Let the actual side - length be $y$ feet. Using the proportion $\frac{5}{200}=\frac{10}{y}$, cross - multiply gives $5y = 200\times10$, so $y = 400$ feet.

Step4: Calculate 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: Determine number of times around the park for 1 mile

1 mile is 5280 feet. Let $n$ be the number of times around the park. Then $n=\frac{5280}{1600}=3.3$ times.

Step6: Calculate actual dimensions of Lafayette Square

For the length of Lafayette Square, if the scale is 1 inch to 200 feet and the map length is 4 inches, the actual length $L = 4\times200=800$ feet.
For the width of Lafayette Square, if the map width is 2.5 inches, the actual width $W = 2.5\times200 = 500$ feet.

Answer:

1. 12.5 centimeters
2. 1600 feet
3. 3.3 times
4. Length: 800 feet, Width: 500 feet