Name: Date: Unit 6: Similar Triangles Homework 1: Ratio & Proportion Bell: 2.30 treadmills to 36 elliptical machines Directions. Write the ratio in simplest form. 1. 28 elementary schools to 16 middle schools EX 10341 To 4 4 3. 18 buses to 66 cars 4. 180 red marbles to 145 blue marbles 6. In the word FLASHLIGHT what is the ratio of vowels to total letters? 5. The hockey team played 82 regular season games last year. If they won 44 games, what is the ratio of wins to losses? Directions: Use the given ratios to solve each problem. Jolye tu 7. The ratio of the measures of two 8. The ratio of the measures of the three angles in complementary angles is 7:8. a triangle is 2:9:4. 9. The ratio of the measures of the three angles in a triangle is 10:3:7. 10. The ratio of the measure of the vertex angle to the base angle of an isosceles triangle is 8:5. 8X45X+5x=180 SSX 11. The ratio of the measures of the sides of a triangle is 21:8:14. If the perimeter of the triangle is 215 feet, find X 12. The ratio of the measures of the sides of a triangle is 4:7:5. If the perimeter of the triangle is 128 yards, find X. Directions: Solve each proportion. 1. I 2 28-24 2 14-X 19.12=10x 228 – 10x JO 10 +-22.8 17 10 | 18. x-163 + 6 5 7. is 2x-2 BIX -20) = 304-11) 18 X-360=4-334366 Ist = 327 is is 21,8
What is the idea behind the question..?
Topic Ratio and Proportion
What is this question about..? This is a math homework assignment on ratios and proportions, specifically on similar triangles. The assignment includes exercises on simplifying ratios, using ratios to solve problems related to angles and sides of triangles, and solving proportions. There are also word problems involving real-world situations.
The correct answer and explanation is:
Here are the answers to the given questions and a 300-word explanation about the topic and solutions:
Answers:
- Simplify 28:1628:16:
2816=74\frac{28}{16} = \frac{7}{4}
Answer: 7:47:4 - Simplify 18:6618:66:
1866=311\frac{18}{66} = \frac{3}{11}
Answer: 3:113:11 - Simplify 180:145180:145:
180145=3629\frac{180}{145} = \frac{36}{29}
Answer: 36:2936:29 - Ratio of vowels in “FLASHLIGHT” to total letters:
Vowels = 2 (A, I); Total letters = 10
Answer: 2:10=1:52:10 = 1:5 - Wins to losses:
Games won = 44, Games lost = 82−44=3882 – 44 = 38
Answer: 44:38=22:1944:38 = 22:19 - For the complementary angles 7:87:8:
Total = 7x+8x=907x + 8x = 90, so 15x=9015x = 90, x=6x = 6
Angles: 7x=42∘7x = 42^\circ, 8x=48∘8x = 48^\circ
Answer: 42∘,48∘42^\circ, 48^\circ - Triangle angles 2:9:42:9:4:
Total = 2x+9x+4x=1802x + 9x + 4x = 180, 15x=18015x = 180, x=12x = 12
Angles: 24∘,108∘,48∘24^\circ, 108^\circ, 48^\circ
Answer: 24∘,108∘,48∘24^\circ, 108^\circ, 48^\circ - Triangle angles 10:3:710:3:7:
Total = 20x=18020x = 180, x=9x = 9
Angles: 90∘,27∘,63∘90^\circ, 27^\circ, 63^\circ
Answer: 90∘,27∘,63∘90^\circ, 27^\circ, 63^\circ - Isosceles triangle:
8x+2(5x)=1808x + 2(5x) = 180, 18x=18018x = 180, x=10x = 10
Angles: 80∘,50∘,50∘80^\circ, 50^\circ, 50^\circ
Answer: 80∘,50∘,50∘80^\circ, 50^\circ, 50^\circ - Triangle sides 21:8:1421:8:14:
Total = 43x=21543x = 215, x=5x = 5
Sides: 105,40,70105, 40, 70
Answer: 105,40,70105, 40, 70 - Triangle sides 4:7:54:7:5:
Total = 16x=12816x = 128, x=8x = 8
Sides: 32,56,4032, 56, 40
Answer: 32,56,4032, 56, 40 - Proportion: Solve as shown in classwork.
Explanation:
Ratios and proportions are foundational concepts in mathematics that allow comparisons between numbers or quantities. A ratio expresses the relationship between two numbers by division. For example, the ratio 28:1628:16 simplifies to 7:47:4 by dividing both terms by their greatest common divisor (GCD).
In proportions, we equate two ratios to solve for unknown values. For instance, to find a missing side in similar triangles, we apply the property that corresponding sides are proportional.
Real-world problems often require applying these concepts. For example, finding the ratio of wins to losses involves comparing two parts of a whole, whereas determining triangle angles uses the total sum property (180∘180^\circ for triangles).
Understanding ratios and proportions develops problem-solving skills and provides tools to address everyday quantitative challenges. This assignment reinforces these principles through step-by-step practice, real-world scenarios, and geometric applications.