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Understanding Ratios and Proportions Through the Lens of Film and Geometry

ariel-moss avatar
ariel-moss
18 diapositives · 327 Views · Nov 20, 2014

Explore how ratios and proportions play a crucial role in both geometry and film production, specifically in the creation of "The Lord of the Rings" movies. Filmmakers relied on precise ratios to build detailed miniature models of Middle-earth, showcasing vast fortresses and cities. This lesson covers the definitions of ratios and proportions, how to express them, and examples involving triangles, rectangles, and real-world applications like scaling drawings or fish tank capacities. Gain insights into solving proportions and the relationship between different measurements.

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  1. 7-1 Ratio and Proportion Holt Geometry

  2. The Lord of the Rings movies transport viewers to the fantasy world of Middle Earth. Many scenes feature vast fortresses, sprawling cities, and bottomless mines. To film these images, the moviemakers used ratios to help them build highly detailed miniature models.

  3. A ratio compares two numbers by division. The ratio of two numbers a and b can be written as a to b, a:b, or , where b ≠ 0.

  4. Write a ratio expressing the slope of l. Substitute the given values. Simplify.

  5. A ratio can involve more than two numbers. For the rectangle, the ratio of the side lengths may be written as 3:7:3:7.

  6. The ratio of the side lengths of a triangle is 4:7:5, and its perimeter is 96 cm. What is the length of the shortest side?

  7. The ratio of the angle measures in a triangle is 1:6:13. What is the measure of each angle?

  8. A proportion is an equation stating that two ratios are equal..

  9. Example 3A: Solving Proportions Solve the proportion.

  10. Example 3B: Solving Proportions Solve the proportion.

  11. Solve the proportion.

  12. The following table shows equivalent forms of the Cross Products Property.

  13. List the equivalent equations to the given proportion.

  14. Given that 18c = 24d, find the ratio of d to c in simplest form. 18c = 24d Divide both sides by 24c. Simplify.

  15. Marta is making a scale drawing of her bedroom. Her rectangular room is 12 1/2 feet wide and 15 feet long. On the scale drawing, the width of her room is 5 inches. What is the length?

  16. For a certain type of tropical fish, it is recommended that you have no more than 2 fish per 10 gallons of water. How many fish could you have in a fish tank that holds 35 gallons of water?

  17. The Titanic was 882 feet 9 inches long. You can build a model of the ship that is 2 feet 6 inches long and 6 inches high. What is the approximate height of the Titanic to the nearest inch?