Finding the Length of the Longer Stick

Oct 13, 2025 by talynt.org 138 views

Understanding the Problem

The problem states that the lengths of two sticks are in the ratio of 11:3. This means that the ratio of the length of the smaller stick to the length of the larger stick is 11:3. We are also given that the smallest stick is 15 cm long. Our goal is to find the length of the longer stick.

Setting Up the Ratio

To solve this problem, we need to set up a ratio using the given information. Let's assume that the length of the smaller stick is 11x and the length of the larger stick is 3x, where x is a constant. Since we know that the smallest stick is 15 cm long, we can set up the equation:

11x = 15

Solving for x

To find the value of x, we can divide both sides of the equation by 11:

x = 15/11

x = 1.36 (approximately)

Finding the Length of the Longer Stick

Now that we have the value of x, we can find the length of the longer stick by multiplying 3x:

Length of the longer stick = 3x = 3(1.36) = 4.08 cm

Conclusion

Therefore, the length of the longer stick is approximately 4.08 cm.

Real-World Applications

This problem may seem simple, but it has real-world applications in various fields such as engineering, architecture, and design. For example, when designing a building, architects need to consider the ratio of the length of the walls to the length of the roof. Similarly, engineers need to consider the ratio of the length of the pipes to the length of the fittings when designing a piping system.

Tips and Tricks

When solving problems involving ratios, it's essential to set up the ratio correctly and to check your units. In this problem, we assumed that the ratio of the length of the smaller stick to the length of the larger stick is 11:3. We also assumed that the length of the smaller stick is 15 cm long. By setting up the ratio correctly and checking our units, we were able to find the length of the longer stick.

Common Mistakes

One common mistake when solving problems involving ratios is to forget to check the units. For example, if we had assumed that the length of the smaller stick was 15 meters long, we would have gotten a different answer. By checking our units, we can ensure that our answer is correct.

Practice Problems

Here are a few practice problems to help you practice solving problems involving ratios:

The lengths of two sticks are in the ratio of 5:2. The smaller stick is 20 cm long. How long is the longer stick?
The lengths of two sticks are in the ratio of 3:4. The smaller stick is 15 cm long. How long is the longer stick?
The lengths of two sticks are in the ratio of 2:5. The smaller stick is 10 cm long. How long is the longer stick?

Solutions to Practice Problems

The lengths of two sticks are in the ratio of 5:2. The smaller stick is 20 cm long. How long is the longer stick? Let's assume that the length of the smaller stick is 5x and the length of the larger stick is 2x, where x is a constant. Since we know that the smaller stick is 20 cm long, we can set up the equation:

5x = 20

To find the value of x, we can divide both sides of the equation by 5:

x = 20/5

x = 4

Now that we have the value of x, we can find the length of the longer stick by multiplying 2x:

Length of the longer stick = 2x = 2(4) = 8 cm

Therefore, the length of the longer stick is 8 cm.

The lengths of two sticks are in the ratio of 3:4. The smaller stick is 15 cm long. How long is the longer stick? Let's assume that the length of the smaller stick is 3x and the length of the larger stick is 4x, where x is a constant. Since we know that the smaller stick is 15 cm long, we can set up the equation:

3x = 15

To find the value of x, we can divide both sides of the equation by 3:

x = 15/3

x = 5

Now that we have the value of x, we can find the length of the longer stick by multiplying 4x:

Length of the longer stick = 4x = 4(5) = 20 cm

Therefore, the length of the longer stick is 20 cm.

The lengths of two sticks are in the ratio of 2:5. The smaller stick is 10 cm long. How long is the longer stick? Let's assume that the length of the smaller stick is 2x and the length of the larger stick is 5x, where x is a constant. Since we know that the smaller stick is 10 cm long, we can set up the equation:

2x = 10

To find the value of x, we can divide both sides of the equation by 2:

x = 10/2

x = 5

Now that we have the value of x, we can find the length of the longer stick by multiplying 5x:

Length of the longer stick = 5x = 5(5) = 25 cm

Therefore, the length of the longer stick is 25 cm.

Q: What is the ratio of the lengths of the two sticks?

A: The ratio of the lengths of the two sticks is 11:3.

Q: What is the length of the smaller stick?

A: The length of the smaller stick is 15 cm.

Q: How do I find the length of the longer stick?

A: To find the length of the longer stick, you need to set up a ratio using the given information. Let's assume that the length of the smaller stick is 11x and the length of the larger stick is 3x, where x is a constant. Since we know that the smaller stick is 15 cm long, we can set up the equation:

11x = 15

Q: How do I solve for x?

A: To find the value of x, you can divide both sides of the equation by 11:

x = 15/11

x = 1.36 (approximately)

Q: How do I find the length of the longer stick?

A: Now that we have the value of x, we can find the length of the longer stick by multiplying 3x:

Length of the longer stick = 3x = 3(1.36) = 4.08 cm

Q: What are some real-world applications of this problem?

A: This problem may seem simple, but it has real-world applications in various fields such as engineering, architecture, and design. For example, when designing a building, architects need to consider the ratio of the length of the walls to the length of the roof. Similarly, engineers need to consider the ratio of the length of the pipes to the length of the fittings when designing a piping system.

Q: What are some common mistakes to avoid when solving this problem?

A: One common mistake when solving problems involving ratios is to forget to check the units. For example, if we had assumed that the length of the smaller stick was 15 meters long, we would have gotten a different answer. By checking our units, we can ensure that our answer is correct.

Q: How can I practice solving problems involving ratios?

A: Here are a few practice problems to help you practice solving problems involving ratios:

The lengths of two sticks are in the ratio of 5:2. The smaller stick is 20 cm long. How long is the longer stick?
The lengths of two sticks are in the ratio of 3:4. The smaller stick is 15 cm long. How long is the longer stick?
The lengths of two sticks are in the ratio of 2:5. The smaller stick is 10 cm long. How long is the longer stick?

Q: What are the solutions to the practice problems?

A: Here are the solutions to the practice problems:

The lengths of two sticks are in the ratio of 5:2. The smaller stick is 20 cm long. How long is the longer stick? Let's assume that the length of the smaller stick is 5x and the length of the larger stick is 2x, where x is a constant. Since we know that the smaller stick is 20 cm long, we can set up the equation:

5x = 20

To find the value of x, we can divide both sides of the equation by 5:

x = 20/5

x = 4

Now that we have the value of x, we can find the length of the longer stick by multiplying 2x:

Length of the longer stick = 2x = 2(4) = 8 cm

Therefore, the length of the longer stick is 8 cm.

The lengths of two sticks are in the ratio of 3:4. The smaller stick is 15 cm long. How long is the longer stick? Let's assume that the length of the smaller stick is 3x and the length of the larger stick is 4x, where x is a constant. Since we know that the smaller stick is 15 cm long, we can set up the equation:

3x = 15

To find the value of x, we can divide both sides of the equation by 3:

x = 15/3

x = 5

Now that we have the value of x, we can find the length of the longer stick by multiplying 4x:

Length of the longer stick = 4x = 4(5) = 20 cm

Therefore, the length of the longer stick is 20 cm.

The lengths of two sticks are in the ratio of 2:5. The smaller stick is 10 cm long. How long is the longer stick? Let's assume that the length of the smaller stick is 2x and the length of the larger stick is 5x, where x is a constant. Since we know that the smaller stick is 10 cm long, we can set up the equation:

2x = 10

To find the value of x, we can divide both sides of the equation by 2:

x = 10/2

x = 5

Now that we have the value of x, we can find the length of the longer stick by multiplying 5x:

Length of the longer stick = 5x = 5(5) = 25 cm

Therefore, the length of the longer stick is 25 cm.