Question

*Which of the following is a Pythagorean triplet ?* 1️⃣ (61, 62, 63 ) 2️⃣ (10 , 60, 61) 3️⃣ (11, 50, 61) 4️⃣ (11, 60, 61)​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given:

Which of the following is a Pythagorean triplet ?* 1️⃣ (61, 62, 63 ) 2️⃣ (10 , 60, 61) 3️⃣ (11, 50, 61) 4️⃣ (11, 60, 61)​

To find:

Which of the following is a Pythagorean triplet?

Solution:

We know,

A Pythagorean Triple consists of three positive integers a, b and c such that

$\boxed{\bold{a^2 + b^2 = c^2}}$

Additional note:- If a triangle's sides are Pythagorean triples then it is a right-angled triangle

Option (1): (61, 62, 63 )

a = 61

b = 62

c = 63

c² = 63² = 3969

a² + b² = 61² + 62² = 3721 + 3844 = 7565

∴ a² + b² ≠ c²

Thus, (61, 62, 63 ) is not a Pythagorean triplet.

Option (2): (10, 60, 61 )

a = 10

b = 60

c = 61

c² = 61² = 3721

a² + b² = 10² + 60² = 100 + 3600 = 3700

∴ a² + b² ≠ c²

Thus, (10 , 60, 61) is not a Pythagorean triplet.

Option (3): (11, 50, 61 )

a = 11

b = 50

c = 61

c² = 61² = 3721

a² + b² = 11² + 50² = 121 + 2500 = 2621

∴ a² + b² ≠ c²

Thus, (11 , 50, 61) is not a Pythagorean triplet.

Option (4): (11, 60, 61 )

a = 11

b = 60

c = 61

c² = 61² = 3721

a² + b² = 11² + 60² = 121 + 3600 = 3721

∴ a² + b² = c²

Thus, $\boxed{\bold{(11 , 60, 61)\: is\: a\: Pythagorean\: triplet.}}$

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