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
![**Solve for \( h \). You must show all steps.**
Given the equation:
\[ A = 2lw + 2wh + 2lh \]
To solve for \( h \), we will start by isolating \( h \) on one side of the equation. Follow the steps below:
1. Combine all terms involving \( h \) on one side of the equation.
\[ A = 2lw + 2wh + 2lh \]
2. Factor out \( h \) from the terms on the right-hand side that contain \( h \).
\[ A = 2lw + h(2w + 2l) \]
3. Isolate \( h \) by subtracting \( 2lw \) from both sides of the equation.
\[ A - 2lw = h(2w + 2l) \]
4. Divide both sides of the equation by \( 2w + 2l \) to solve for \( h \).
\[ h = \frac{A - 2lw}{2w + 2l} \]
Thus, the solution for \( h \) is:
\[ h = \frac{A - 2lw}{2w + 2l} \]
Explanation of Symbols:
- \( A \) represents the total area.
- \( l \) represents the length.
- \( w \) represents the width.
- \( h \) represents the height.
**Conclusion:**
By following the above steps, we isolate the variable \( h \) and express it in terms of \( A \), \( l \), and \( w \). This solution can be applied to various problems where you need to solve for the height given the area and other dimensions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fcdecb9-56df-4c9c-aece-60df7fbe5b7a%2F42c28e99-95d5-4e93-b423-8a141c3e5367%2F61molw_processed.png&w=3840&q=75)
Transcribed Image Text:**Solve for \( h \). You must show all steps.**
Given the equation:
\[ A = 2lw + 2wh + 2lh \]
To solve for \( h \), we will start by isolating \( h \) on one side of the equation. Follow the steps below:
1. Combine all terms involving \( h \) on one side of the equation.
\[ A = 2lw + 2wh + 2lh \]
2. Factor out \( h \) from the terms on the right-hand side that contain \( h \).
\[ A = 2lw + h(2w + 2l) \]
3. Isolate \( h \) by subtracting \( 2lw \) from both sides of the equation.
\[ A - 2lw = h(2w + 2l) \]
4. Divide both sides of the equation by \( 2w + 2l \) to solve for \( h \).
\[ h = \frac{A - 2lw}{2w + 2l} \]
Thus, the solution for \( h \) is:
\[ h = \frac{A - 2lw}{2w + 2l} \]
Explanation of Symbols:
- \( A \) represents the total area.
- \( l \) represents the length.
- \( w \) represents the width.
- \( h \) represents the height.
**Conclusion:**
By following the above steps, we isolate the variable \( h \) and express it in terms of \( A \), \( l \), and \( w \). This solution can be applied to various problems where you need to solve for the height given the area and other dimensions.
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