Explain if a triangle with the given lengths is a right triangle.
1. 18, 24, 30
2. 7, 24, 25
3. 13, 14, 15
4. 8, 15, 17
5. 10,24, 25
6. 15, 36, 39
Are my answers correct? Thanks.
1. yes
2. yes
3. no because 19. 10497 cannot be a triangle. Also, 19.10497 is not equal to 15.
4. yes
5. no because 26 isn't equal to 25
6. yes
Great! All are correct!
thanks!!!!!!!
You're welcome.
To determine if a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's apply this theorem to each given triangle:
1. The lengths are 18, 24, and 30. To determine if it is a right triangle, we need to check if 18^2 + 24^2 = 30^2 is true. Evaluating this equation, we have 324 + 576 = 900, which is true. Therefore, it is a right triangle.
2. The lengths are 7, 24, and 25. We check if 7^2 + 24^2 = 25^2 is true. Evaluating this equation, we have 49 + 576 = 625, which is true. Therefore, it is a right triangle.
3. The given lengths are 13, 14, and 15. However, the explanation you provided seems incorrect. To check if it is a right triangle, we calculate 13^2 + 14^2 and find that it is equal to 365, not 19.10497. Therefore, it is not a right triangle.
4. The lengths are 8, 15, and 17. Checking if 8^2 + 15^2 = 17^2 is true, we find that 64 + 225 = 289, which is true. Therefore, it is a right triangle.
5. The lengths are 10, 24, and 25. However, you mentioned that 26 isn't equal to 25, but it should be 24^2. Checking if 10^2 + 24^2 = 25^2 is true, we find that 100 + 576 = 625, which is true. Therefore, it is a right triangle.
6. The lengths are 15, 36, and 39. Checking if 15^2 + 36^2 = 39^2 is true, we find that 225 + 1296 = 1521, which is true. Therefore, it is a right triangle.
To summarize, the correct answers are:
1. yes, it is a right triangle.
2. yes, it is a right triangle.
3. no, it is not a right triangle.
4. yes, it is a right triangle.
5. yes, it is a right triangle.
6. yes, it is a right triangle.