Read The Problem Carefully. Solve In Your Notebook And Type In The Correct Letter Below.Answer Must Be A Single Capital Letter.Clue 8Which Set Of Side Lengths Do Not Form A Right Triangle?A. 7, 24, 25 B. $11.2, 21, \frac{119}{5}$ C.
Introduction
In mathematics, a right triangle is a triangle in which one of the angles is a right angle (90 degrees). The side lengths of a right triangle follow the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this problem, we are given three sets of side lengths and asked to determine which set does not form a right triangle.
Understanding the Pythagorean Theorem
The Pythagorean theorem is a fundamental concept in geometry and trigonometry. It is expressed mathematically as:
a^2 + b^2 = c^2
where a and b are the lengths of the two sides that form the right angle, and c is the length of the hypotenuse. This theorem can be used to determine whether a triangle is a right triangle or not.
Analyzing the Given Sets of Side Lengths
We are given three sets of side lengths:
A. 7, 24, 25 B. 11.2, 21, 119/5 C. (missing)
To determine which set does not form a right triangle, we need to apply the Pythagorean theorem to each set.
Set A: 7, 24, 25
Let's assume that 7 and 24 are the two sides that form the right angle, and 25 is the length of the hypotenuse. We can plug these values into the Pythagorean theorem:
7^2 + 24^2 = 25^2 49 + 576 = 625 625 = 625
Since the equation holds true, we can conclude that set A does form a right triangle.
Set B: 11.2, 21, 119/5
Let's assume that 11.2 and 21 are the two sides that form the right angle, and 119/5 is the length of the hypotenuse. We can plug these values into the Pythagorean theorem:
11.2^2 + 21^2 = (119/5)^2 125.44 + 441 = 254.44 566.44 ≠ 254.44
Since the equation does not hold true, we can conclude that set B does not form a right triangle.
Set C: (missing)
Since set C is missing, we cannot determine whether it forms a right triangle or not.
Conclusion
Based on our analysis, we can conclude that set B (11.2, 21, 119/5) does not form a right triangle. The other two sets, A (7, 24, 25) and C (missing), may or may not form a right triangle, depending on the values of the missing set.
Discussion
This problem requires careful analysis and application of the Pythagorean theorem. It is essential to understand the concept of right triangles and how to use the Pythagorean theorem to determine whether a triangle is a right triangle or not. The problem also highlights the importance of checking the given information carefully, as a small mistake can lead to incorrect conclusions.
Final Answer
The final answer is B.
Introduction
In our previous article, we solved the problem of determining which set of side lengths does not form a right triangle. We analyzed three sets of side lengths and applied the Pythagorean theorem to each set. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information on the topic.
Q&A
Q: What is the Pythagorean theorem?
A: The Pythagorean theorem is a fundamental concept in geometry and trigonometry that states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It is expressed mathematically as:
a^2 + b^2 = c^2
where a and b are the lengths of the two sides that form the right angle, and c is the length of the hypotenuse.
Q: How do I apply the Pythagorean theorem to a set of side lengths?
A: To apply the Pythagorean theorem to a set of side lengths, you need to identify the two sides that form the right angle and the length of the hypotenuse. Then, you can plug these values into the Pythagorean theorem and check if the equation holds true.
Q: What if the equation does not hold true?
A: If the equation does not hold true, it means that the set of side lengths does not form a right triangle.
Q: Can a triangle have more than one right angle?
A: No, a triangle can only have one right angle. If a triangle has more than one right angle, it is not a valid triangle.
Q: Can a right triangle have all sides of equal length?
A: No, a right triangle cannot have all sides of equal length. If a triangle has all sides of equal length, it is an equilateral triangle, not a right triangle.
Q: How do I determine the length of the hypotenuse?
A: To determine the length of the hypotenuse, you can use the Pythagorean theorem. If you know the lengths of the two sides that form the right angle, you can plug these values into the Pythagorean theorem and solve for the length of the hypotenuse.
Q: Can I use the Pythagorean theorem to find the length of a side?
A: Yes, you can use the Pythagorean theorem to find the length of a side. If you know the lengths of the other two sides, you can plug these values into the Pythagorean theorem and solve for the length of the unknown side.
Conclusion
In this Q&A article, we provided answers to common questions related to the Pythagorean theorem and right triangles. We hope that this article has helped to clarify any doubts and provide additional information on the topic.
Final Answer
The final answer is B.
Additional Resources
- Pythagorean Theorem Calculator: A calculator that can help you calculate the length of the hypotenuse or the length of a side using the Pythagorean theorem.
- Right Triangle Calculator: A calculator that can help you determine if a triangle is a right triangle or not.
- Geometry and Trigonometry Tutorials: A collection of tutorials that can help you learn more about geometry and trigonometry, including the Pythagorean theorem and right triangles.