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)

A (4, 5, 6)

B (10, 24, 26)

C (18, 24, 35)

D (25, 144, 169)

E (21, 72, 75)

Answer 1

To determine which of the given sets are Pythagorean triples, we can use the Pythagorean theorem, which states that for a right triangle with sides \(a\), \(b\), and hypotenuse \(c\), the relationship \(a^2 + b^2 = c^2\) must hold true.

Let's evaluate each option:

A. **(4, 5, 6)**
- Here \( c = 6 \), \( a = 4 \), \( b = 5 \).
- \(4^2 + 5^2 = 16 + 25 = 41\)
- \(6^2 = 36\)
- **Not a Pythagorean triple.**

B. **(10, 24, 26)**
- Here \( c = 26 \), \( a = 10 \), \( b = 24 \).
- \(10^2 + 24^2 = 100 + 576 = 676\)
- \(26^2 = 676\)
- **This is a Pythagorean triple.**

C. **(18, 24, 35)**
- Here \( c = 35 \), \( a = 18 \), \( b = 24 \).
- \(18^2 + 24^2 = 324 + 576 = 900\)
- \(35^2 = 1225\)
- **Not a Pythagorean triple.**

D. **(25, 144, 169)**
- Here \( c = 169 \), \( a = 25 \), \( b = 144 \).
- \(25^2 + 144^2 = 625 + 20736 = 21361\)
- \(169^2 = 28561\)
- **Not a Pythagorean triple.**

E. **(21, 72, 75)**
- Here \( c = 75 \), \( a = 21 \), \( b = 72 \).
- \(21^2 + 72^2 = 441 + 5184 = 5625\)
- \(75^2 = 5625\)
- **This is a Pythagorean triple.**

In summary, the Pythagorean triples from the lists provided are:

- **B (10, 24, 26)**
- **E (21, 72, 75)**