A Painting's Length Is 10 Meters More Than Its Width W W W . What Function Represents The Painting's Area A ( W A(w A ( W ]?A. A ( W ) = 10 W A(w) = 10w A ( W ) = 10 W B. A ( W ) = W 2 − 10 W A(w) = W^2 - 10w A ( W ) = W 2 − 10 W C. A ( W ) = W 2 + 10 W A(w) = W^2 + 10w A ( W ) = W 2 + 10 W D. A ( W ) = W 2 + 10 A(w) = W^2 + 10 A ( W ) = W 2 + 10

Introduction

When it comes to calculating the area of a painting, it's essential to understand the relationship between its length and width. In this article, we'll explore how to represent the painting's area as a function of its width, and we'll examine the different options provided to determine the correct function.

The Relationship Between Length and Width

The problem states that the painting's length is 10 meters more than its width, denoted as $w$. This means that the length can be represented as $w + 10$. To find the area of the painting, we need to multiply the length and width together.

Calculating the Area

The area of a rectangle, such as a painting, is calculated by multiplying its length and width. In this case, the length is $w + 10$ and the width is $w$. Therefore, the area $A(w)$ can be represented as:

$$A(w) = (w + 10) \cdot w$$

Simplifying the Expression

To simplify the expression, we can use the distributive property to multiply the terms:

$$A(w) = w^2 + 10w$$

Comparing the Options

Now that we have the correct expression for the area, let's compare it to the options provided:

A. $A(w) = 10w$ B. $A(w) = w^2 - 10w$ C. $A(w) = w^2 + 10w$ D. $A(w) = w^2 + 10$

Analyzing the Options

Option A is incorrect because it only includes the term $10w$, which is missing the squared term $w^2$. Option B is also incorrect because it includes a negative term $-10w$, which is not present in our simplified expression. Option D is incorrect because it includes a constant term $+10$, which is not present in our simplified expression.

Conclusion

Based on our analysis, the correct function that represents the painting's area $A(w)$ is:

$$A(w) = w^2 + 10w$$

This function accurately represents the relationship between the painting's length and width, and it provides a clear and concise way to calculate the area of the painting.

Real-World Applications

Understanding the relationship between a painting's length and width has practical applications in various fields, such as:

• Art and Design: When creating a piece of art, artists need to consider the proportions and dimensions of their work. By understanding the relationship between length and width, artists can create balanced and visually appealing compositions.
• Architecture: Architects need to consider the dimensions and proportions of buildings, bridges, and other structures. By understanding the relationship between length and width, architects can design structures that are safe, functional, and aesthetically pleasing.
• Engineering: Engineers need to consider the dimensions and proportions of machines, mechanisms, and other devices. By understanding the relationship between length and width, engineers can design devices that are efficient, reliable, and safe.

Conclusion

In conclusion, understanding the relationship between a painting's length and width is essential for calculating its area. By using the correct function, $A(w) = w^2 + 10w$, we can accurately represent the area of the painting and apply this knowledge to various real-world applications.

Final Thoughts

The relationship between a painting's length and width is a fundamental concept in mathematics that has practical applications in various fields. By understanding this relationship, we can create balanced and visually appealing compositions, design safe and functional structures, and develop efficient and reliable devices.

Introduction

In our previous article, we explored the relationship between a painting's length and width, and we determined that the area of the painting can be represented by the function $A(w) = w^2 + 10w$. In this article, we'll answer some frequently asked questions about this topic.

Q: What is the relationship between a painting's length and width?

A: The problem states that the painting's length is 10 meters more than its width, denoted as $w$. This means that the length can be represented as $w + 10$.

Q: How do I calculate the area of a painting?

A: To calculate the area of a painting, you need to multiply its length and width together. In this case, the length is $w + 10$ and the width is $w$. Therefore, the area $A(w)$ can be represented as:

$$A(w) = (w + 10) \cdot w$$

Q: What is the correct function that represents the painting's area?

A: The correct function that represents the painting's area is:

$$A(w) = w^2 + 10w$$

Q: Why is option A incorrect?

A: Option A is incorrect because it only includes the term $10w$, which is missing the squared term $w^2$.

Q: Why is option B incorrect?

A: Option B is incorrect because it includes a negative term $-10w$, which is not present in our simplified expression.

Q: Why is option D incorrect?

A: Option D is incorrect because it includes a constant term $+10$, which is not present in our simplified expression.

Q: What are some real-world applications of understanding the relationship between a painting's length and width?

A: Understanding the relationship between a painting's length and width has practical applications in various fields, such as:

• Art and Design: When creating a piece of art, artists need to consider the proportions and dimensions of their work. By understanding the relationship between length and width, artists can create balanced and visually appealing compositions.
• Architecture: Architects need to consider the dimensions and proportions of buildings, bridges, and other structures. By understanding the relationship between length and width, architects can design structures that are safe, functional, and aesthetically pleasing.
• Engineering: Engineers need to consider the dimensions and proportions of machines, mechanisms, and other devices. By understanding the relationship between length and width, engineers can design devices that are efficient, reliable, and safe.

Q: What are some tips for calculating the area of a painting?

A: Here are some tips for calculating the area of a painting:

• Make sure to multiply the length and width together: To calculate the area of a painting, you need to multiply its length and width together.
• Use the correct function: The correct function that represents the painting's area is $A(w) = w^2 + 10w$.
• Check your units: Make sure to check your units to ensure that they are consistent.

Conclusion

In conclusion, understanding the relationship between a painting's length and width is essential for calculating its area. By using the correct function, $A(w) = w^2 + 10w$, we can accurately represent the area of the painting and apply this knowledge to various real-world applications.

Final Thoughts

The relationship between a painting's length and width is a fundamental concept in mathematics that has practical applications in various fields. By understanding this relationship, we can create balanced and visually appealing compositions, design safe and functional structures, and develop efficient and reliable devices.