Question

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)

Answer 1

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)