The Table Shows The Lengths Of Picket Fence Pieces Jude Has To Make A Flower Garden. He Wants The Garden To Have 4 Sides And A Perimeter Of 30 Feet. He Cannot Cut The Pieces Into Smaller Lengths.$\[ \begin{tabular}{|l|l|} \hline \text{Fence Length}

Feb 28, 2025 by ADMIN 249 views

Introduction

Mathematics in Real-Life Scenarios: Mathematics is not just a subject in school, but it is also a vital tool used in various real-life scenarios. One such scenario is when we need to calculate the perimeter of a fence to create a flower garden. In this article, we will discuss how to use the given table to find the lengths of picket fence pieces Jude has to make a flower garden with a perimeter of 30 feet.

Problem Description

Jude wants to create a flower garden with 4 sides and a perimeter of 30 feet. He has a table with different lengths of picket fence pieces, but he cannot cut the pieces into smaller lengths. The table is as follows:

Length	Number of Pieces
3 feet	4
5 feet	3
7 feet	2
9 feet	1

Step 1: Understanding the Problem

To solve this problem, we need to understand that the perimeter of a fence is the total distance around the fence. Since Jude wants to create a flower garden with 4 sides, we can assume that the fence will be a rectangle with 4 equal sides.

Step 2: Calculating the Perimeter

The perimeter of a rectangle is calculated by adding the lengths of all its sides. Since Jude wants the perimeter to be 30 feet, we can set up an equation:

4x = 30

where x is the length of each side.

Step 3: Solving for x

To solve for x, we can divide both sides of the equation by 4:

x = 30/4 x = 7.5

Step 4: Finding the Combination of Fence Pieces

Since Jude cannot cut the pieces into smaller lengths, we need to find a combination of the given lengths that adds up to 7.5 feet. We can start by trying different combinations of the given lengths:

3 feet + 3 feet + 3 feet + 3 feet = 12 feet (too long)
5 feet + 5 feet + 5 feet = 15 feet (too long)
7 feet + 7 feet = 14 feet (too long)
9 feet + 3 feet + 3 feet + 3 feet = 18 feet (too long)

However, we can try a combination of 5 feet and 3 feet:

5 feet + 3 feet + 3 feet + 3 feet = 14 feet (too long)
5 feet + 5 feet + 3 feet + 3 feet = 16 feet (too long)
5 feet + 5 feet + 5 feet + 3 feet = 18 feet (too long)
5 feet + 5 feet + 5 feet + 5 feet = 20 feet (too long)
5 feet + 5 feet + 3 feet + 3 feet + 3 feet + 3 feet = 18 feet (too long)
5 feet + 3 feet + 3 feet + 3 feet + 3 feet + 3 feet = 15 feet (too long)
5 feet + 5 feet + 3 feet + 3 feet + 3 feet + 3 feet + 3 feet = 22 feet (too long)
5 feet + 5 feet + 5 feet + 3 feet + 3 feet + 3 feet + 3 feet + 3 feet = 26 feet (too long)
5 feet + 5 feet + 5 feet + 5 feet + 3 feet + 3 feet + 3 feet + 3 feet = 28 feet (too long)
5 feet + 5 feet + 5 feet + 5 feet + 5 feet + 3 feet + 3 feet + 3 feet = 30 feet (just right)

Step 5: Conclusion

Based on the calculations, we can see that Jude needs 6 pieces of 5 feet and 2 pieces of 3 feet to create a flower garden with a perimeter of 30 feet.

Conclusion

In this article, we discussed how to use the given table to find the lengths of picket fence pieces Jude has to make a flower garden with a perimeter of 30 feet. We calculated the perimeter of the fence, found the combination of fence pieces that adds up to 7.5 feet, and concluded that Jude needs 6 pieces of 5 feet and 2 pieces of 3 feet to create the garden.

Discussion

This problem is a great example of how mathematics is used in real-life scenarios. It requires us to think critically and use problem-solving skills to find the solution. The problem also highlights the importance of being able to work with different units of measurement and to be able to convert between them.

Final Answer

The final answer is 6 pieces of 5 feet and 2 pieces of 3 feet.

Introduction

In our previous article, we discussed how to use the given table to find the lengths of picket fence pieces Jude has to make a flower garden with a perimeter of 30 feet. In this article, we will answer some frequently asked questions related to the problem.

Q1: What is the perimeter of a fence?

A1: The perimeter of a fence is the total distance around the fence. It is calculated by adding the lengths of all its sides.

Q2: How do I calculate the perimeter of a rectangle?

A2: To calculate the perimeter of a rectangle, you need to add the lengths of all its sides. Since a rectangle has 4 equal sides, you can use the formula: Perimeter = 2(l + w), where l is the length and w is the width.

Q3: What is the length of each side of the fence?

A3: To find the length of each side of the fence, we need to divide the perimeter by 4. In this case, the perimeter is 30 feet, so the length of each side is 30/4 = 7.5 feet.

Q4: How do I find the combination of fence pieces that adds up to 7.5 feet?

A4: To find the combination of fence pieces that adds up to 7.5 feet, we need to try different combinations of the given lengths. We can start by trying different combinations of the given lengths and see which one adds up to 7.5 feet.

Q5: What is the final answer?

A5: The final answer is 6 pieces of 5 feet and 2 pieces of 3 feet.

Q6: Why can't Jude cut the pieces into smaller lengths?

A6: Jude cannot cut the pieces into smaller lengths because the problem states that he cannot cut the pieces into smaller lengths.

Q7: What is the importance of being able to work with different units of measurement?

A7: Being able to work with different units of measurement is important because it allows us to convert between different units and to solve problems that involve different units.

Q8: How does this problem relate to real-life scenarios?

A8: This problem relates to real-life scenarios because it involves calculating the perimeter of a fence, which is a common task in construction and landscaping.

Q9: What are some other examples of problems that involve calculating the perimeter of a shape?

A9: Some other examples of problems that involve calculating the perimeter of a shape include calculating the perimeter of a circle, calculating the perimeter of a triangle, and calculating the perimeter of a polygon.

Q10: How can I practice solving problems like this one?

A10: You can practice solving problems like this one by trying different combinations of lengths and seeing which one adds up to the desired perimeter. You can also try solving problems that involve calculating the perimeter of different shapes.

Conclusion

In this article, we answered some frequently asked questions related to the problem of finding the lengths of picket fence pieces Jude has to make a flower garden with a perimeter of 30 feet. We hope that this article has been helpful in understanding the problem and in solving similar problems in the future.

Discussion

Final Answer

The final answer is 6 pieces of 5 feet and 2 pieces of 3 feet.