Leo wants to paint a mural that covers a wall with an area of 800 square feet. The height of the wall is of its length. 2 What is the length and the height of the wall? So, the dimensions (length by height) of the wall are feet by feet.
Leo wants to paint a mural that covers a wall with an area of 800 square feet. The height of the wall is of its length. 2 What is the length and the height of the wall? So, the dimensions (length by height) of the wall are feet by feet.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter5: Rational Numbers And Equations
Section5.5: Dividing Fractions
Problem 28E
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![### Problem Statement
Leo wants to paint a mural that covers a wall with an area of 800 square feet. The height of the wall is \( \frac{1}{2} \) of its length.
**Question:** What is the length and the height of the wall?
**Solution:**
Let \( L \) represent the length of the wall in feet.
Then, the height \( H \) of the wall is \( \frac{1}{2} \) of the length:
\[ H = \frac{1}{2}L \]
The area \( A \) of the wall is given by the product of its length and height:
\[ A = L \cdot H \]
Substituting the given values:
\[ 800 = L \cdot \frac{1}{2}L \]
\[ 800 = \frac{1}{2}L^2 \]
Solving for \( L \):
\[ 800 \cdot 2 = L^2 \]
\[ 1600 = L^2 \]
\[ L = \sqrt{1600} \]
\[ L = 40 \text{ feet} \]
The height \( H \) is:
\[ H = \frac{1}{2} \cdot 40 \]
\[ H = 20 \text{ feet} \]
So, the dimensions (length by height) of the wall are 40 feet by 20 feet.
### Interactive Solution Boxes
**Dimensions (length by height) of the wall:**
- **Length:** [40] feet
- **Height:** [20] feet
Feel free to use these dimensions for your mural project!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38e6b8ef-5aec-4a21-80bf-35b048951448%2F2edc9c45-6ca4-48ad-9111-4fe602d1dbec%2Fsrgvjyp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Leo wants to paint a mural that covers a wall with an area of 800 square feet. The height of the wall is \( \frac{1}{2} \) of its length.
**Question:** What is the length and the height of the wall?
**Solution:**
Let \( L \) represent the length of the wall in feet.
Then, the height \( H \) of the wall is \( \frac{1}{2} \) of the length:
\[ H = \frac{1}{2}L \]
The area \( A \) of the wall is given by the product of its length and height:
\[ A = L \cdot H \]
Substituting the given values:
\[ 800 = L \cdot \frac{1}{2}L \]
\[ 800 = \frac{1}{2}L^2 \]
Solving for \( L \):
\[ 800 \cdot 2 = L^2 \]
\[ 1600 = L^2 \]
\[ L = \sqrt{1600} \]
\[ L = 40 \text{ feet} \]
The height \( H \) is:
\[ H = \frac{1}{2} \cdot 40 \]
\[ H = 20 \text{ feet} \]
So, the dimensions (length by height) of the wall are 40 feet by 20 feet.
### Interactive Solution Boxes
**Dimensions (length by height) of the wall:**
- **Length:** [40] feet
- **Height:** [20] feet
Feel free to use these dimensions for your mural project!
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