Pregunta
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A specific park is rectangular-shaped and has a 3 -mile perimeter. The length is 4 times the width. What are the dimensions (in miles) of the park? width length SUBMIT ANSWER

Ask by Simpson Weber. in the United States
Mar 14,2025

Solución de inteligencia artificial de Upstudy

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Width: 0.3 miles Length: 1.2 miles

Solución

**Step 1: Define the variables** Let the width be \( w \) miles. Since the length is 4 times the width, the length can be written as \( 4w \) miles. **Step 2: Write the formula for the perimeter** The formula for the perimeter \( P \) of a rectangle is given by: \[ P = 2(\text{width} + \text{length}) \] For this park, this becomes: \[ 3 = 2(w + 4w) \] **Step 3: Simplify the equation** Combine like terms inside the parentheses: \[ 3 = 2(5w) \] This simplifies to: \[ 3 = 10w \] **Step 4: Solve for \( w \)** Divide both sides by 10: \[ w = \frac{3}{10} \] **Step 5: Determine the length** Since the length is 4 times the width: \[ \text{Length} = 4w = 4 \left( \frac{3}{10} \right) = \frac{12}{10} = \frac{6}{5} \] **Final Answer:** - Width: \( \frac{3}{10} \) miles - Length: \( \frac{6}{5} \) miles

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Mind Expander

Let's dive into some fun math to uncover those park dimensions! To start, let's use the perimeter formula for a rectangle, which is \( P = 2(length + width) \). Given that the perimeter is 3 miles, we can set up our equation as \( 2(L + W) = 3 \). Moreover, since the length \( L \) is 4 times the width \( W \), we express it as \( L = 4W \). Replacing \( L \) in the perimeter equation gives us \( 2(4W + W) = 3 \), or \( 10W = 3 \). Thus, the width \( W \) becomes \( 0.3 \) miles and the length \( L \) as \( 4W = 1.2 \) miles. Now we have it: the width of the park is 0.3 miles and the length is 1.2 miles. Perfect for a serene stroll! 🌳 For those who love exploring math, this problem highlights how shapes can be formed from ratios and relationships. You can expand your knowledge by solving similar perimeter problems with varying ratios. Next time, try using different multiplication factors, and see what shapes you can create! It’s a great way to sharpen your skills while having fun with numbers!

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