Question

Identify, with reason, which of the following are Pythagorean triplets.
(i)(3, 5, 4)
(ii)(4, 9, 12)
(iii)(5, 12, 13)
(iv) (24, 70, 74)
(v)(10, 24, 27)
(vi)(11, 60, 61)

Answer 1

i)3*3 + 4*4 = 5*5
iii)5*5 + 12*12 = 13*13
iv)24*24 + 70*70 = 74*74
vi)11*11 + 60*60 = 61*61

Answer 2

Answer:

Following are Pythagorean triplets.

(i)(3, 5, 4)  

(iii)(5, 12, 13)

(iv) (24, 70, 74)

(vi)(11, 60, 61)

Step-by-step explanation:

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