Question
Rosanna calculates that the length of c is 225 in. What needs to be correct in her calculation?
(1 point)
Responses
Rosanna's answer is right because she correctly applied the Pythagorean Theorem
Rosanna's answer is right because she correctly applied the Pythagorean Theorem
Rosanna mistakenly added the squared hypotenuse with the square of the longest leg instead of adding both squared legs
Rosanna mistakenly added the squared hypotenuse with the square of the longest leg instead of adding both squared legs
Rosanna should take the square root of the sum when using the Pythagorean Theorem
Rosanna should take the square root of the sum when using the Pythagorean Theorem
Rosanna forgot to divide the answer she found through the Pythagorean Theorem by 2.
Answers
Answered by
GPT-4o mini
To determine what needs to be corrected in Rosanna's calculation, we should consider how the Pythagorean Theorem works. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
Mathematically, it is expressed as:
\[ c^2 = a^2 + b^2 \]
Given that Rosanna calculated the length of c as 225 inches, we must analyze the possible responses:
1. **Rosanna's answer is right because she correctly applied the Pythagorean Theorem.**
- This response is only valid if her value of c was indeed correct and derived correctly.
2. **Rosanna mistakenly added the squared hypotenuse with the square of the longest leg instead of adding both squared legs.**
- This response suggests she misunderstood how to apply the theorem.
3. **Rosanna should take the square root of the sum when using the Pythagorean Theorem.**
- In the process of using the theorem, she would take the square root only after summing the squares of the legs, not beforehand.
4. **Rosanna forgot to divide the answer she found through the Pythagorean Theorem by 2.**
- This response does not relate to the application of the Pythagorean theorem.
The most fitting response would depend on the context of her calculation and whether she found c correctly. If her calculation involved erroneous steps such as not adding the squares of both legs or failing to take the square root correctly, the correct response would point out those mistakes.
However, without specific details on how she arrived at her answer, we can't ascertain the reason definitively. If we assume she made a mistake in using the theorem, the most appropriate response would likely be:
**Rosanna should take the square root of the sum when using the Pythagorean Theorem.**
This suggests she might have made a calculation error in arriving at c.
Mathematically, it is expressed as:
\[ c^2 = a^2 + b^2 \]
Given that Rosanna calculated the length of c as 225 inches, we must analyze the possible responses:
1. **Rosanna's answer is right because she correctly applied the Pythagorean Theorem.**
- This response is only valid if her value of c was indeed correct and derived correctly.
2. **Rosanna mistakenly added the squared hypotenuse with the square of the longest leg instead of adding both squared legs.**
- This response suggests she misunderstood how to apply the theorem.
3. **Rosanna should take the square root of the sum when using the Pythagorean Theorem.**
- In the process of using the theorem, she would take the square root only after summing the squares of the legs, not beforehand.
4. **Rosanna forgot to divide the answer she found through the Pythagorean Theorem by 2.**
- This response does not relate to the application of the Pythagorean theorem.
The most fitting response would depend on the context of her calculation and whether she found c correctly. If her calculation involved erroneous steps such as not adding the squares of both legs or failing to take the square root correctly, the correct response would point out those mistakes.
However, without specific details on how she arrived at her answer, we can't ascertain the reason definitively. If we assume she made a mistake in using the theorem, the most appropriate response would likely be:
**Rosanna should take the square root of the sum when using the Pythagorean Theorem.**
This suggests she might have made a calculation error in arriving at c.