Question

Which of the following is a Pythagorean triplet?

(3, 4, 5)

(5, 6, 7)

(7, 8, 9)​

Answer 1

Answer:

(3,4,5) is the Pythagorean triplet

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Answer 2

Procedure:

• To verify if any given 3 numbers is a Pythagorean triplet or not, substitute the value of the 3 numbers in Pythagoras theorem formula.
• Hypotenuse is always the longest side in a right angled triangle.
• Pythagoras theorem states that:

(Hypotenuse)² = (Sum of squares of other 2 sides)

Solution:

a. (3, 4, 5)

Length of maximum side = 5 → Hypotenuse

By Pythagoras theorem,

(5)² = (3)² + (4)²

⇒ 25 = 9 + 16

⇒ 25 = 25

Hence, (3, 4, 5) form a Pythagorean triplet.

b. (5, 6, 7)

Length of maximum side = 7 → Hypotenuse

By Pythagoras theorem,

(7)² = (5)² + (6)²

⇒ 49 = 25 + 36

But, 49 ≠ 61

Hence, (5, 6, 7) doesn't form a Pythagorean triplet.

c. (7, 8, 9)

Length of maximum side = 9 → Hypotenuse

By Pythagoras theorem,

(9)² = (7)² + (8)²

⇒ 81 = 49 + 64

But, 81 ≠ 113

Hence, (7, 8, 9) doesn't form a Pythagorean triplet.