Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter3: Math Models
Section3.4: Solve Geometry Applications: Triangles, Rectangles, And The Pythagorean Theorem
Problem 3.74TI: One angle of a right triangle measures 45°. What is the measure of the other small angle?
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Transcribed Image Text:What is the value for x for the two triangles below that would make the two triangles similar?
16
B
12
E 8 F
O24
18
О 26
O 12
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What is the value for x for the two
![**Problem Statement:**
What is the value for \( x \) for the two triangles below that would make the two triangles similar?
**Explanation with Diagram:**
There are two triangles given in the diagram:
1. **Triangle ABC:**
- Side AB = 24
- Side BC = unknown (\( x \))
- No value provided for side AC
2. **Triangle DEF:**
- Side DE = 10
- Side EF = 18
- No value provided for side DF
The triangles are oriented similarly, implying that corresponding sides are proportional. To find the value of \( x \) that makes the two triangles similar, we must set up a proportion between corresponding sides of the triangles.
### Proportion Setup:
1. Corresponding sides AB (24) in Triangle ABC and DE (10) in Triangle DEF.
2. Corresponding sides BC (\( x \)) in Triangle ABC and EF (18) in Triangle DEF.
As the sides should be proportional for similarity, we use the following proportion relationships:
\[ \frac{AB}{DE} = \frac{BC}{EF} \]
Plug in the known values:
\[ \frac{24}{10} = \frac{x}{18} \]
Solving this for \( x \):
\[ 24 \cdot 18 = 10 \cdot x \]
\[ 432 = 10x \]
\[ x = \frac{432}{10} \]
\[ x = 43.2 \]
### Conclusion:
The value for \( x \) that would make the two triangles similar is \( 43.2 \).](https://content.bartleby.com/qna-images/question/9d0c88f8-9b0e-4a87-ae6c-39dd67e2599b/43bd4615-9520-4887-91bf-d9c591a134f4/8buhehd_processed.jpeg)
Transcribed Image Text:**Problem Statement:**
What is the value for \( x \) for the two triangles below that would make the two triangles similar?
**Explanation with Diagram:**
There are two triangles given in the diagram:
1. **Triangle ABC:**
- Side AB = 24
- Side BC = unknown (\( x \))
- No value provided for side AC
2. **Triangle DEF:**
- Side DE = 10
- Side EF = 18
- No value provided for side DF
The triangles are oriented similarly, implying that corresponding sides are proportional. To find the value of \( x \) that makes the two triangles similar, we must set up a proportion between corresponding sides of the triangles.
### Proportion Setup:
1. Corresponding sides AB (24) in Triangle ABC and DE (10) in Triangle DEF.
2. Corresponding sides BC (\( x \)) in Triangle ABC and EF (18) in Triangle DEF.
As the sides should be proportional for similarity, we use the following proportion relationships:
\[ \frac{AB}{DE} = \frac{BC}{EF} \]
Plug in the known values:
\[ \frac{24}{10} = \frac{x}{18} \]
Solving this for \( x \):
\[ 24 \cdot 18 = 10 \cdot x \]
\[ 432 = 10x \]
\[ x = \frac{432}{10} \]
\[ x = 43.2 \]
### Conclusion:
The value for \( x \) that would make the two triangles similar is \( 43.2 \).
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