Real-world examples of similar objects and scale factor

📚 Quick Study Guide

• 📏 Similar Objects: Objects that have the same shape but different sizes.
• 📐 Corresponding Sides: Sides in similar objects that are in the same relative position.
• 🔢 Scale Factor: The ratio of the length of a side in one object to the length of the corresponding side in a similar object. If the scale factor is greater than 1, it's an enlargement. If it's less than 1, it's a reduction.
• ➗ Calculating Scale Factor: $\text{Scale Factor} = \frac{\text{Length of side in new object}}{\text{Length of corresponding side in original object}}$
• 💡 Using Scale Factor: To find the length of a side in a similar object, multiply the length of the corresponding side in the original object by the scale factor.
• 🗺️ Applications: Architecture, maps, model building, and photography.

Practice Quiz

1. Which of the following is an example of similar objects?
   1. A basketball and a tennis ball.
   2. A square with side length 2cm and a square with side length 4cm.
   3. A triangle and a square.
   4. A cube and a pyramid.
2. A map of a city is made using a scale factor of 1:10,000. If a park is 5 cm long on the map, what is its actual length in meters?
   1. 50 m
   2. 500 m
   3. 5000 m
   4. 5 m
3. A photo is enlarged from 4x6 inches to 8x12 inches. What is the scale factor of the enlargement?
   1. 1/2
   2. 2
   3. 4
   4. 1
4. A model car is built with a scale factor of 1:24. If the real car is 4.8 meters long, how long is the model car in centimeters?
   1. 2 cm
   2. 20 cm
   3. 200 cm
   4. 0.2 cm
5. Two similar triangles have corresponding sides of length 5cm and 15cm. What is the scale factor?
   1. 3
   2. 1/3
   3. 5
   4. 1/5
6. A blueprint of a house uses a scale of 1 inch = 2 feet. If a room is shown as 12 inches long on the blueprint, how long is the actual room in feet?
   1. 6 feet
   2. 12 feet
   3. 24 feet
   4. 36 feet
7. A rectangular garden is 10m long and 5m wide. A similar garden is created with a scale factor of 2. What is the area of the new garden?
   1. 50 $m^2$
   2. 100 $m^2$
   3. 200 $m^2$
   4. 400 $m^2$