Using the Perimeter Formula to Find Side b

Oct 13, 2025 by windailys.com 126 views

A scalene triangle is a type of triangle where all sides are of different lengths. In this article, we will explore the concept of the perimeter of a scalene triangle and how to use it to find the value of one side when the lengths of the other two sides are known.

What is the Perimeter of a Triangle?

The perimeter of a triangle is the sum of the lengths of all its sides. It is a fundamental concept in geometry and is used to calculate the total distance around a triangle. The formula for the perimeter of a triangle is:

P = a + b + c

where P is the perimeter, and a, b, and c are the lengths of the sides.

Understanding the Problem

In this problem, we are given that the perimeter of a scalene triangle is 54.6 cm, and one of the sides, denoted as a, measures 8.7 cm. We are asked to find the value of side b.

Using the Perimeter Formula to Find Side b

To find the value of side b, we can use the perimeter formula and substitute the given values. We know that the perimeter is 54.6 cm, and one of the sides, a, measures 8.7 cm. We can set up an equation using the perimeter formula:

P = a + b + c

Substituting the given values, we get:

54.6 = 8.7 + b + c

However, we are not given the value of side c. But we can simplify the equation by subtracting 8.7 from both sides:

45.9 = b + c

Finding the Value of Side b

Since we are not given the value of side c, we cannot find the exact value of side b using the equation above. However, we can express side b in terms of side c:

b = 45.9 - c

But we are given three options to choose from. Let's analyze each option and see which one matches the equation above.

Analyzing the Options

Option A: 8.7 + b = 54.6

Subtracting 8.7 from both sides, we get:

b = 45.9

This option does not match the equation above, as it does not include side c.

Option B: 17.4 + b = 54.6

Subtracting 17.4 from both sides, we get:

b = 37.2

This option does not match the equation above, as it does not include side c.

Option C: 26.1 + b = 54.6

Subtracting 26.1 from both sides, we get:

b = 28.5

This option does not match the equation above, as it does not include side c.

However, we can try to find a combination of options that matches the equation above. Let's try to add the values of options A and B:

Option A: 8.7 + b = 54.6 Option B: 17.4 + b = 54.6

Adding the values of options A and B, we get:

26.1 + b = 54.6

This option matches the equation above, as it includes side c.

Conclusion

In conclusion, the correct equation to find the value of side b is:

26.1 + b = 54.6

This equation matches the perimeter formula and includes side c. Therefore, the correct answer is option C.

Final Answer

In the previous article, we explored the concept of the perimeter of a scalene triangle and how to use it to find the value of one side when the lengths of the other two sides are known. In this article, we will answer some frequently asked questions (FAQs) about the perimeter of a scalene triangle.

Q: What is the perimeter of a triangle?

A: The perimeter of a triangle is the sum of the lengths of all its sides. It is a fundamental concept in geometry and is used to calculate the total distance around a triangle.

Q: How do I find the perimeter of a scalene triangle?

A: To find the perimeter of a scalene triangle, you need to add the lengths of all three sides. The formula for the perimeter of a triangle is:

P = a + b + c

where P is the perimeter, and a, b, and c are the lengths of the sides.

Q: What is a scalene triangle?

A: A scalene triangle is a type of triangle where all sides are of different lengths. This means that none of the sides are equal in length.

Q: How do I find the value of one side of a scalene triangle when the lengths of the other two sides are known?

A: To find the value of one side of a scalene triangle when the lengths of the other two sides are known, you can use the perimeter formula and substitute the given values. For example, if the perimeter is 54.6 cm and one of the sides, a, measures 8.7 cm, you can set up an equation using the perimeter formula:

P = a + b + c

Substituting the given values, you get:

54.6 = 8.7 + b + c

However, you are not given the value of side c. But you can simplify the equation by subtracting 8.7 from both sides:

45.9 = b + c

Q: How do I find the value of side b in the equation b + c = 45.9?

A: To find the value of side b in the equation b + c = 45.9, you need to know the value of side c. However, you are not given the value of side c. But you can express side b in terms of side c:

b = 45.9 - c

Q: What is the relationship between the perimeter of a triangle and its sides?

A: The perimeter of a triangle is the sum of the lengths of all its sides. This means that the perimeter is equal to the sum of the lengths of the three sides.

Q: Can I use the perimeter formula to find the value of one side of a scalene triangle when the lengths of the other two sides are known?

A: Yes, you can use the perimeter formula to find the value of one side of a scalene triangle when the lengths of the other two sides are known. However, you need to know the value of the other two sides and the perimeter.

Q: What is the formula for the perimeter of a triangle?

A: The formula for the perimeter of a triangle is:

P = a + b + c

where P is the perimeter, and a, b, and c are the lengths of the sides.

Conclusion

In conclusion, the perimeter of a scalene triangle is the sum of the lengths of all its sides. To find the value of one side of a scalene triangle when the lengths of the other two sides are known, you can use the perimeter formula and substitute the given values. We hope that this article has helped to answer some of the frequently asked questions about the perimeter of a scalene triangle.