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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)

1 answer

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)