Asked by wewoowewoo
Select the Pythagorean triples.
(Hint: plug them into the Pythagorean theorem to see if they work. Remember c is always the greatest value in the set)
(4, 5, 6)
(10, 24, 26)
(25, 144, 169)
(21, 72, 75)
(18, 24, 35)
(Hint: plug them into the Pythagorean theorem to see if they work. Remember c is always the greatest value in the set)
(4, 5, 6)
(10, 24, 26)
(25, 144, 169)
(21, 72, 75)
(18, 24, 35)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To verify which of the provided sets of numbers are Pythagorean triples, we will use the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the largest number in each triplet.
Let's check each set:
1. **(4, 5, 6)**
Here, \( a = 4 \), \( b = 5 \), and \( c = 6 \).
\[ 4^2 + 5^2 = 16 + 25 = 41 \]
\[ 6^2 = 36 \]
Not a triple.
2. **(10, 24, 26)**
Here, \( a = 10 \), \( b = 24 \), and \( c = 26 \).
\[ 10^2 + 24^2 = 100 + 576 = 676 \]
\[ 26^2 = 676 \]
This is a Pythagorean triple.
3. **(25, 144, 169)**
Here, \( a = 25 \), \( b = 144 \), and \( c = 169 \).
\[ 25^2 + 144^2 = 625 + 20736 = 21361 \]
\[ 169^2 = 28561 \]
Not a triple.
4. **(21, 72, 75)**
Here, \( a = 21 \), \( b = 72 \), and \( c = 75 \).
\[ 21^2 + 72^2 = 441 + 5184 = 5625 \]
\[ 75^2 = 5625 \]
This is a Pythagorean triple.
5. **(18, 24, 35)**
Here, \( a = 18 \), \( b = 24 \), and \( c = 35 \).
\[ 18^2 + 24^2 = 324 + 576 = 900 \]
\[ 35^2 = 1225 \]
Not a triple.
### Summary of Pythagorean Triples
The sets that are Pythagorean triples are:
- (10, 24, 26)
- (21, 72, 75)
\[ a^2 + b^2 = c^2 \]
where \( c \) is the largest number in each triplet.
Let's check each set:
1. **(4, 5, 6)**
Here, \( a = 4 \), \( b = 5 \), and \( c = 6 \).
\[ 4^2 + 5^2 = 16 + 25 = 41 \]
\[ 6^2 = 36 \]
Not a triple.
2. **(10, 24, 26)**
Here, \( a = 10 \), \( b = 24 \), and \( c = 26 \).
\[ 10^2 + 24^2 = 100 + 576 = 676 \]
\[ 26^2 = 676 \]
This is a Pythagorean triple.
3. **(25, 144, 169)**
Here, \( a = 25 \), \( b = 144 \), and \( c = 169 \).
\[ 25^2 + 144^2 = 625 + 20736 = 21361 \]
\[ 169^2 = 28561 \]
Not a triple.
4. **(21, 72, 75)**
Here, \( a = 21 \), \( b = 72 \), and \( c = 75 \).
\[ 21^2 + 72^2 = 441 + 5184 = 5625 \]
\[ 75^2 = 5625 \]
This is a Pythagorean triple.
5. **(18, 24, 35)**
Here, \( a = 18 \), \( b = 24 \), and \( c = 35 \).
\[ 18^2 + 24^2 = 324 + 576 = 900 \]
\[ 35^2 = 1225 \]
Not a triple.
### Summary of Pythagorean Triples
The sets that are Pythagorean triples are:
- (10, 24, 26)
- (21, 72, 75)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.