### Exercise: Finding the Perimeter of an Equilateral Triangle **Problem Statement:** 4. Find the perimeter of a triangle that has equal sides of \( \frac{3}{4} \) in. **Solution Explanation:** To find the perimeter of an equilateral triangle (a triangle with all three sides equal), you simply add up the lengths of all three sides. Since each side of this triangle is \( \frac{3}{4} \) inches, you can calculate the perimeter using the following steps: **Step-by-step Solution:** 1. **Understand the Problem:** - Each side of the triangle is \( \frac{3}{4} \) inches. 2. **Write Down the Formula for the Perimeter of a Triangle:** \[ \text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3} \] 3. **Substitute the Given Values:** \[ \text{Perimeter} = \left( \frac{3}{4} \text{ in} \right) + \left( \frac{3}{4} \text{ in} \right) + \left( \frac{3}{4} \text{ in} \right) \] 4. **Perform the Addition:** Since all the sides are equal: \[ \text{Perimeter} = 3 \times \left( \frac{3}{4} \text{ in} \right) \] 5. **Calculate the Final Value:** \[ \text{Perimeter} = \frac{9}{4} \text{ in} \] Convert \( \frac{9}{4} \text{ in} \) to a mixed number if necessary: \[ \frac{9}{4} \text{ in} = 2 \frac{1}{4} \text{ in} \] **Final Answer:** The perimeter of the triangle is \( 2 \frac{1}{4} \) inches. This example demonstrates how to find the perimeter of an equilateral triangle given the length of its sides. By repeating the same steps, you can solve similar problems with different side lengths.
### Exercise: Finding the Perimeter of an Equilateral Triangle **Problem Statement:** 4. Find the perimeter of a triangle that has equal sides of \( \frac{3}{4} \) in. **Solution Explanation:** To find the perimeter of an equilateral triangle (a triangle with all three sides equal), you simply add up the lengths of all three sides. Since each side of this triangle is \( \frac{3}{4} \) inches, you can calculate the perimeter using the following steps: **Step-by-step Solution:** 1. **Understand the Problem:** - Each side of the triangle is \( \frac{3}{4} \) inches. 2. **Write Down the Formula for the Perimeter of a Triangle:** \[ \text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3} \] 3. **Substitute the Given Values:** \[ \text{Perimeter} = \left( \frac{3}{4} \text{ in} \right) + \left( \frac{3}{4} \text{ in} \right) + \left( \frac{3}{4} \text{ in} \right) \] 4. **Perform the Addition:** Since all the sides are equal: \[ \text{Perimeter} = 3 \times \left( \frac{3}{4} \text{ in} \right) \] 5. **Calculate the Final Value:** \[ \text{Perimeter} = \frac{9}{4} \text{ in} \] Convert \( \frac{9}{4} \text{ in} \) to a mixed number if necessary: \[ \frac{9}{4} \text{ in} = 2 \frac{1}{4} \text{ in} \] **Final Answer:** The perimeter of the triangle is \( 2 \frac{1}{4} \) inches. This example demonstrates how to find the perimeter of an equilateral triangle given the length of its sides. By repeating the same steps, you can solve similar problems with different side lengths.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![### Exercise: Finding the Perimeter of an Equilateral Triangle
**Problem Statement:**
4. Find the perimeter of a triangle that has equal sides of \( \frac{3}{4} \) in.
**Solution Explanation:**
To find the perimeter of an equilateral triangle (a triangle with all three sides equal), you simply add up the lengths of all three sides. Since each side of this triangle is \( \frac{3}{4} \) inches, you can calculate the perimeter using the following steps:
**Step-by-step Solution:**
1. **Understand the Problem:**
- Each side of the triangle is \( \frac{3}{4} \) inches.
2. **Write Down the Formula for the Perimeter of a Triangle:**
\[
\text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3}
\]
3. **Substitute the Given Values:**
\[
\text{Perimeter} = \left( \frac{3}{4} \text{ in} \right) + \left( \frac{3}{4} \text{ in} \right) + \left( \frac{3}{4} \text{ in} \right)
\]
4. **Perform the Addition:**
Since all the sides are equal:
\[
\text{Perimeter} = 3 \times \left( \frac{3}{4} \text{ in} \right)
\]
5. **Calculate the Final Value:**
\[
\text{Perimeter} = \frac{9}{4} \text{ in}
\]
Convert \( \frac{9}{4} \text{ in} \) to a mixed number if necessary:
\[
\frac{9}{4} \text{ in} = 2 \frac{1}{4} \text{ in}
\]
**Final Answer:**
The perimeter of the triangle is \( 2 \frac{1}{4} \) inches.
This example demonstrates how to find the perimeter of an equilateral triangle given the length of its sides. By repeating the same steps, you can solve similar problems with different side lengths.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa2bd4a1-658a-407d-88ce-b68f7d21ec93%2Fdedef25c-beff-4c54-b05b-fcc1f24a4083%2Fvlij5vp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exercise: Finding the Perimeter of an Equilateral Triangle
**Problem Statement:**
4. Find the perimeter of a triangle that has equal sides of \( \frac{3}{4} \) in.
**Solution Explanation:**
To find the perimeter of an equilateral triangle (a triangle with all three sides equal), you simply add up the lengths of all three sides. Since each side of this triangle is \( \frac{3}{4} \) inches, you can calculate the perimeter using the following steps:
**Step-by-step Solution:**
1. **Understand the Problem:**
- Each side of the triangle is \( \frac{3}{4} \) inches.
2. **Write Down the Formula for the Perimeter of a Triangle:**
\[
\text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3}
\]
3. **Substitute the Given Values:**
\[
\text{Perimeter} = \left( \frac{3}{4} \text{ in} \right) + \left( \frac{3}{4} \text{ in} \right) + \left( \frac{3}{4} \text{ in} \right)
\]
4. **Perform the Addition:**
Since all the sides are equal:
\[
\text{Perimeter} = 3 \times \left( \frac{3}{4} \text{ in} \right)
\]
5. **Calculate the Final Value:**
\[
\text{Perimeter} = \frac{9}{4} \text{ in}
\]
Convert \( \frac{9}{4} \text{ in} \) to a mixed number if necessary:
\[
\frac{9}{4} \text{ in} = 2 \frac{1}{4} \text{ in}
\]
**Final Answer:**
The perimeter of the triangle is \( 2 \frac{1}{4} \) inches.
This example demonstrates how to find the perimeter of an equilateral triangle given the length of its sides. By repeating the same steps, you can solve similar problems with different side lengths.
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