Asked by _behindyou_
Which are perfect squares? Select the four correct answers.(4 points) Responses 200 200 16 16 625 625 24 24 169 169 9
Which side lengths would form a right triangle?(1 point) Responses 30, 24, & 18 30, 24, & 18 21, 16, & 12 21, 16, & 12 9, 12, & 14 9, 12, & 14 24, 7, & 26 24, 7, & 26
What is the value of x if 13, 84, x is a Pythagorean triple?(1 point) Responses 85 85 97 97 94 94 86
Elinor determined that a triangle with side lengths 6, 10, and 8 does not form a right triangle using the following steps: 6^2+10^2=8^2 36+100=64 136≠64 Is her answer correct? (1 point) Responses No, she should've added 10^2 and 8^2 and compared that to 6^2. No, she should've added 6^2 and 8^2 and compared that to 10^2. Yes, she is correct. No, she should've added 6^2 from 10^2 and compared that to 8^2.
Which side lengths would form a right triangle?(1 point) Responses 30, 24, & 18 30, 24, & 18 21, 16, & 12 21, 16, & 12 9, 12, & 14 9, 12, & 14 24, 7, & 26 24, 7, & 26
What is the value of x if 13, 84, x is a Pythagorean triple?(1 point) Responses 85 85 97 97 94 94 86
Elinor determined that a triangle with side lengths 6, 10, and 8 does not form a right triangle using the following steps: 6^2+10^2=8^2 36+100=64 136≠64 Is her answer correct? (1 point) Responses No, she should've added 10^2 and 8^2 and compared that to 6^2. No, she should've added 6^2 and 8^2 and compared that to 10^2. Yes, she is correct. No, she should've added 6^2 from 10^2 and compared that to 8^2.
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Answered by
GPT-4o mini
Let's go through each question one by one.
1. **Which are perfect squares?**
- Perfect squares are numbers that can be expressed as the square of an integer.
- The perfect squares from the list are:
- \(16\) (since \(4^2 = 16\))
- \(625\) (since \(25^2 = 625\))
- \(169\) (since \(13^2 = 169\))
- \(9\) (since \(3^2 = 9\))
- Therefore, the correct answers are **16, 625, 169, and 9**.
2. **Which side lengths would form a right triangle?**
- To check each set of numbers, we can use the Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c\) is the largest number.
- For the combinations:
- \(30, 24, & 18\): \(30^2 = 900\), \(24^2 = 576\), \(18^2 = 324\); \(900 \neq 576 + 324\) (not a right triangle)
- \(21, 16, & 12\): \(21^2 = 441\), \(16^2 = 256\), \(12^2 = 144\); \(441 \neq 256 + 144\) (not a right triangle)
- \(9, 12, & 14\): \(14^2 = 196\), \(12^2 = 144\), \(9^2 = 81\); \(196 \neq 144 + 81\) (not a right triangle)
- \(24, 7, & 26\): \(26^2 = 676\), \(24^2 = 576\), \(7^2 = 49\); \(676 = 576 + 49\) (this is a right triangle)
- Therefore, the answer is **24, 7, & 26**.
3. **What is the value of x if 13, 84, x is a Pythagorean triple?**
- We can use the Pythagorean theorem again, where \(x\) must satisfy \(13^2 + 84^2 = x^2\).
- Calculate:
- \(13^2 = 169\) and \(84^2 = 7056\).
- Therefore, \(x^2 = 169 + 7056 = 7225\).
- Taking the square root gives \(x = 85\) (since \(85^2 = 7225\)).
- Therefore, the correct answer is **85**.
4. **Is Elinor's answer correct?**
- Elinor is testing if the triangle is a right triangle by checking if \(6^2 + 10^2 = 8^2\).
- Let's evaluate:
- \(6^2 + 10^2 = 36 + 100 = 136\) and \(8^2 = 64\).
- Since \(136 \neq 64\), her conclusion that it does not form a right triangle is correct.
- Therefore, the answer is **Yes, she is correct**.
So the answers for each question are:
1. 16, 625, 169, 9
2. 24, 7, & 26
3. 85
4. Yes, she is correct.
1. **Which are perfect squares?**
- Perfect squares are numbers that can be expressed as the square of an integer.
- The perfect squares from the list are:
- \(16\) (since \(4^2 = 16\))
- \(625\) (since \(25^2 = 625\))
- \(169\) (since \(13^2 = 169\))
- \(9\) (since \(3^2 = 9\))
- Therefore, the correct answers are **16, 625, 169, and 9**.
2. **Which side lengths would form a right triangle?**
- To check each set of numbers, we can use the Pythagorean theorem \(a^2 + b^2 = c^2\), where \(c\) is the largest number.
- For the combinations:
- \(30, 24, & 18\): \(30^2 = 900\), \(24^2 = 576\), \(18^2 = 324\); \(900 \neq 576 + 324\) (not a right triangle)
- \(21, 16, & 12\): \(21^2 = 441\), \(16^2 = 256\), \(12^2 = 144\); \(441 \neq 256 + 144\) (not a right triangle)
- \(9, 12, & 14\): \(14^2 = 196\), \(12^2 = 144\), \(9^2 = 81\); \(196 \neq 144 + 81\) (not a right triangle)
- \(24, 7, & 26\): \(26^2 = 676\), \(24^2 = 576\), \(7^2 = 49\); \(676 = 576 + 49\) (this is a right triangle)
- Therefore, the answer is **24, 7, & 26**.
3. **What is the value of x if 13, 84, x is a Pythagorean triple?**
- We can use the Pythagorean theorem again, where \(x\) must satisfy \(13^2 + 84^2 = x^2\).
- Calculate:
- \(13^2 = 169\) and \(84^2 = 7056\).
- Therefore, \(x^2 = 169 + 7056 = 7225\).
- Taking the square root gives \(x = 85\) (since \(85^2 = 7225\)).
- Therefore, the correct answer is **85**.
4. **Is Elinor's answer correct?**
- Elinor is testing if the triangle is a right triangle by checking if \(6^2 + 10^2 = 8^2\).
- Let's evaluate:
- \(6^2 + 10^2 = 36 + 100 = 136\) and \(8^2 = 64\).
- Since \(136 \neq 64\), her conclusion that it does not form a right triangle is correct.
- Therefore, the answer is **Yes, she is correct**.
So the answers for each question are:
1. 16, 625, 169, 9
2. 24, 7, & 26
3. 85
4. Yes, she is correct.
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