A 5-inch By 7-inch Photograph Is Placed Inside A Picture Frame. Both The Length And Width Of The Frame Are $2x$ Inches Larger Than The Width And Length Of The Photograph. Which Expression Represents The Perimeter Of The Frame?A. $4x +

In this problem, we are given a 5-inch by 7-inch photograph placed inside a picture frame. The length and width of the frame are $2x$ inches larger than the width and length of the photograph. Our goal is to find the expression that represents the perimeter of the frame.

Breaking Down the Problem

To solve this problem, we need to understand the concept of perimeter and how it relates to the dimensions of the frame. The perimeter of a shape is the distance around the shape, and it can be calculated by adding up the lengths of all its sides.

Calculating the Dimensions of the Frame

Let's start by calculating the dimensions of the frame. Since the length and width of the frame are $2x$ inches larger than the width and length of the photograph, we can calculate the dimensions of the frame as follows:

• Length of the frame: $7 + 2x$
• Width of the frame: $5 + 2x$

Calculating the Perimeter of the Frame

Now that we have the dimensions of the frame, we can calculate its perimeter. The perimeter of a rectangle (such as the frame) is given by the formula:

Perimeter = 2(Length + Width)

Substituting the values we calculated earlier, we get:

Perimeter = 2((7 + 2x) + (5 + 2x)) Perimeter = 2(12 + 4x) Perimeter = 24 + 8x

Conclusion

Therefore, the expression that represents the perimeter of the frame is $24 + 8x$. This expression takes into account the dimensions of the frame and the additional $2x$ inches added to both the length and width of the photograph.

Discussion

This problem requires a basic understanding of algebra and geometry. The key concept here is to understand how to calculate the perimeter of a shape and how to apply algebraic expressions to solve problems.

Example Use Case

This problem can be applied to real-world scenarios such as designing picture frames or calculating the dimensions of a frame for a specific photograph.

Step-by-Step Solution

Here's a step-by-step solution to the problem:

1. Calculate the dimensions of the frame by adding $2x$ inches to the length and width of the photograph.
2. Calculate the perimeter of the frame using the formula: Perimeter = 2(Length + Width)
3. Substitute the values calculated in step 1 into the formula in step 2.
4. Simplify the expression to get the final answer.

Key Concepts

• Perimeter: The distance around a shape.
• Algebraic expressions: Mathematical expressions that involve variables and constants.
• Geometry: The branch of mathematics that deals with the study of shapes and their properties.

Common Mistakes

• Failing to calculate the dimensions of the frame correctly.
• Failing to apply the formula for perimeter correctly.
• Failing to simplify the expression correctly.

Real-World Applications

• Designing picture frames for specific photographs.
• Calculating the dimensions of a frame for a specific photograph.
• Understanding the concept of perimeter and how it applies to real-world scenarios.
  A 5-inch by 7-inch Photograph in a Picture Frame: Q&A ===========================================================

In our previous article, we explored the problem of a 5-inch by 7-inch photograph placed inside a picture frame, where the length and width of the frame are $2x$ inches larger than the width and length of the photograph. We calculated the expression that represents the perimeter of the frame as $24 + 8x$. In this article, we will answer some frequently asked questions related to this problem.

Q: What is the perimeter of the frame when x = 0?

A: When x = 0, the perimeter of the frame is 24 + 8(0) = 24.

Q: What is the perimeter of the frame when x = 1?

A: When x = 1, the perimeter of the frame is 24 + 8(1) = 32.

Q: How do I calculate the perimeter of the frame if the length and width of the photograph are different?

A: To calculate the perimeter of the frame if the length and width of the photograph are different, you can follow the same steps as before. However, you will need to calculate the dimensions of the frame separately for the length and width of the photograph.

Q: Can I use this formula to calculate the perimeter of any shape?

A: No, this formula is specifically designed to calculate the perimeter of a rectangle (such as a picture frame). If you need to calculate the perimeter of a different shape, you will need to use a different formula.

Q: What is the relationship between the perimeter of the frame and the dimensions of the photograph?

A: The perimeter of the frame is directly proportional to the dimensions of the photograph. As the dimensions of the photograph increase, the perimeter of the frame also increases.

Q: Can I use this formula to calculate the area of the frame?

A: No, this formula is specifically designed to calculate the perimeter of the frame. If you need to calculate the area of the frame, you will need to use a different formula.

Q: How do I calculate the area of the frame if the length and width of the photograph are different?

A: To calculate the area of the frame if the length and width of the photograph are different, you can use the formula: Area = Length x Width. You will need to calculate the dimensions of the frame separately for the length and width of the photograph.

Q: What is the significance of the variable x in this problem?

A: The variable x represents the additional inches added to the length and width of the photograph to create the frame.

Q: Can I use this formula to calculate the perimeter of a frame with a different shape?

A: No, this formula is specifically designed to calculate the perimeter of a rectangular frame. If you need to calculate the perimeter of a frame with a different shape, you will need to use a different formula.

Q: How do I apply this formula in real-world scenarios?

A: You can apply this formula in real-world scenarios such as designing picture frames, calculating the dimensions of a frame for a specific photograph, or understanding the concept of perimeter and how it applies to real-world scenarios.

Conclusion

In this article, we answered some frequently asked questions related to the problem of a 5-inch by 7-inch photograph placed inside a picture frame. We hope that this article has provided you with a better understanding of the problem and its applications.