Pregunta
Rob makes a scale drawing of a horse barm. The scale of the drawing is 1 inch : 5 yards. The barn has an area of 8 square inches in the drawing. What is the area of the barn in real life? square yards
Ask by Ramirez Summers. in the United States
Jan 06,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The barn's real-life area is 200 square yards.
Solución
To determine the real-life area of the barn based on the scale drawing, follow these steps:
1. **Understand the Scale:**
- **Scale Given:** 1 inch (drawing) : 5 yards (real life)
2. **Area Scaling Factor:**
- When scaling areas, you square the linear scale factor.
- **Linear Scale Factor:** 5 yards per 1 inch
- **Area Scale Factor:** \(5^2 = 25\) square yards per square inch
3. **Calculate Real-Life Area:**
- **Area in Drawing:** 8 square inches
- **Real-Life Area:** \(8 \text{ square inches} \times 25 \text{ square yards/square inch} = 200 \text{ square yards}\)
**Answer:** The barn has a real-life area of **200 square yards**.
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To find the real-life area of the barn from the scale drawing, you need to apply the scale factor. Since 1 inch represents 5 yards, the area in real life would be calculated by squaring the scale factor because we are dealing with area. So, (5 yards)² = 25 square yards for every 1 square inch. Now, if the drawing has an area of 8 square inches, you multiply 8 by 25. That gives you an area of 200 square yards for the barn in real life! Remember that when you're working with measurements and scales, always check if you need to square your conversion factor for area, as it's a common step often overlooked! It’s not just about length; area takes into account both dimensions!
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