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)

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)

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