Question

out of the following which is the pythagorean triplet a) 11,60,61 b)4,9,12 c) 10,24,27 b)5,5,2​

Answer 1

Answer:

to be Pythagorean triplets.

Hypotenuse² = Base² + height²

Hypotenuse is largest side in triangle

(i)(3, 5, 4)   iff  5² = 3² + 4² => 25 = 9 + 16 => 25 = 25  - True

(ii)(4, 9, 12)   iff 12² = 9² + 4² => 144 = 81 + 16 but  144 ≠ 97 so False

(iii)(5, 12, 13)  iff  13² = 12² + 5² => 169 = 144 + 26 =>169 = 169  - True

(iv) (24, 70, 74)   iff  74² = 70² + 24² => 5476 = 4900 + 576 =>5476 = 5476  - True

(v)(10, 24, 27)   iff 27² = 24² + 10² =>729 = 576 + 100 but  729 ≠ 676 so False

(vi)(11, 60, 61) iff  61² = 60² + 11² => 3721 = 3600 + 121 =>3721 = 3721  - True

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

a) 11 , 60 , 61

• 61² = 3721
• 11² = 121
• 60² = 3600

:. 3600 + 121 = 3721

• (a) 11 , 60 , 61 is a Pythagorean triplet ✅

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b) 4 , 9 , 12

• 4² = 16
• 9² = 81
• 12² = 144

:. 16 + 81 = 97 ≠ 144

:. 4 , 9 , 12 are not Pythagorean triplet

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c) 10 , 24 , 27

• 10² = 100
• 24² = 576
• 27² = 729

:. 100 + 576 = 676 ≠ 729

:. 10 , 24 , 27 are not Pythagorean triplet

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d) 5 , 5 , 2

• 5² = 25
• 5² = 25
• 2² = 4

:. 25 + 4 = 29 ≠ 25

:. 5 , 5 , 2 are not Pythagorean triplet

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