### Problem StatementLeo 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] feetFeel free to use these dimensions for your mural project!

Answered: Image /qna-images/answer/2edc9c45-6ca4-48ad-9111-4fe602d1dbec.jpg

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.

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

### 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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