A Rectangular Pan Has A Length That Is 4 3 \frac{4}{3} 3 4 ​ The Width. The Total Area Of The Pan Is 432 In 2 ^2 2 . What Is The Width Of The Cake Pan?A. 10.4 In B. 13.9 In C. 18 In D. 24 In

Introduction

When dealing with geometric shapes, understanding the relationships between their dimensions is crucial. In this case, we're given a rectangular pan with a specific ratio between its length and width. We're also provided with the total area of the pan, which is 432 in$^2$. Our goal is to find the width of the pan using this information.

Understanding the Problem

Let's denote the width of the pan as $w$. According to the problem, the length of the pan is $\frac{4}{3}$ times the width. Therefore, we can express the length as $\frac{4}{3}w$. The area of a rectangle is given by the formula $A = lw$, where $A$ is the area, $l$ is the length, and $w$ is the width.

Setting Up the Equation

We know that the total area of the pan is 432 in$^2$, so we can set up the equation:

$$\frac{4}{3}w \cdot w = 432$$

Simplifying the equation, we get:

$$\frac{4}{3}w^2 = 432$$

Solving for $w$

To solve for $w$, we need to isolate $w$ on one side of the equation. First, let's multiply both sides by $\frac{3}{4}$ to get rid of the fraction:

$$w^2 = 432 \cdot \frac{3}{4}$$

$$w^2 = 324$$

Now, we take the square root of both sides to find $w$:

$$w = \sqrt{324}$$

$$w = 18$$

Conclusion

Using the given ratio between the length and width of the pan, and the total area of the pan, we were able to find the width of the pan. The width of the pan is 18 in.

Discussion

This problem requires a good understanding of geometric shapes and their properties. The ratio between the length and width of the pan is a key piece of information that helps us solve the problem. Additionally, the area of the pan is used to set up an equation that we can solve to find the width.

Final Answer

The final answer is $\boxed{18}$ in.

Introduction

In our previous article, we explored how to find the width of a rectangular pan given its length and width ratio, and total area. We're now going to take it a step further by answering some common questions related to this topic.

Q: What is the formula for the area of a rectangle?

A: The formula for the area of a rectangle is $A = lw$, where $A$ is the area, $l$ is the length, and $w$ is the width.

Q: How do I find the length of the pan if I know the width and the ratio between the length and width?

A: If you know the width and the ratio between the length and width, you can find the length by multiplying the width by the ratio. For example, if the width is 18 in and the ratio is $\frac{4}{3}$, the length would be $\frac{4}{3} \cdot 18 = 24$ in.

Q: What if I know the length and the ratio between the length and width, but not the width? How do I find the width?

A: If you know the length and the ratio between the length and width, you can find the width by dividing the length by the ratio. For example, if the length is 24 in and the ratio is $\frac{4}{3}$, the width would be $\frac{24}{\frac{4}{3}} = 18$ in.

Q: Can I use the same method to find the width of a square?

A: No, the method we used to find the width of the rectangular pan does not apply to squares. This is because the ratio between the length and width of a square is 1, not $\frac{4}{3}$.

Q: What if I have a rectangular pan with a length that is $\frac{3}{4}$ the width, and the total area is 324 in$^2$? How do I find the width?

A: To find the width, you can use the same method we used in the previous article. First, set up the equation $\frac{3}{4}w \cdot w = 324$. Simplifying the equation, you get $\frac{3}{4}w^2 = 324$. Multiply both sides by $\frac{4}{3}$ to get rid of the fraction, and then take the square root of both sides to find $w$.

Q: Can I use this method to find the width of any rectangular pan?

A: Yes, as long as you know the ratio between the length and width, and the total area of the pan, you can use this method to find the width.

Q: What if I have a rectangular pan with a length that is $\frac{5}{6}$ the width, and the total area is 540 in$^2$? How do I find the width?

A: To find the width, you can use the same method we used in the previous article. First, set up the equation $\frac{5}{6}w \cdot w = 540$. Simplifying the equation, you get $\frac{5}{6}w^2 = 540$. Multiply both sides by $\frac{6}{5}$ to get rid of the fraction, and then take the square root of both sides to find $w$.

Conclusion

We've answered some common questions related to finding the width of a rectangular pan given its length and width ratio, and total area. By following the steps outlined in this article, you should be able to find the width of any rectangular pan.

Final Answer

The final answer is $\boxed{18}$ in.