Question

Find a Pythagorean triplet with one of the number as 80.

Answer 1

$\huge{\underline{\color{silver}{\textsf{\textbf{~~~Answer}}}}}$

$\sqrt{ ({80})^{2} + (1599 ^{2} )} = 1601$

Therefore 80, 1599 and 1601 are the Pythagorean triplet.

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Answer 2

Answer:   18 , 80 , 82 .            OR          80 , 1599 , 1601 .

Step-by-step explanation:Two Pythagorean triplets are possible with the number 80.

Case(1) : If 2m = 80

=> 2m = 8

=> m = 80/2

=> m = 40

Thus,

=> m² - 1 = 40² - 1

=> m² - 1 = 1600 - 1

=> m² - 1 = 1599

Also,

=> m² + 1 = 40² + 1

=> m² + 1 = 1600 + 1

=> m² + 1 = 1601

Hence,

Required Pythagorean triplet is :

80 , 1599 , 1601 .

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°

Case(2) : If m² - 1 = 80

=> m² - 1 = 80

=> m² = 80 + 1

=> m² = 81

=> m = √81

=> m = 9

Thus,

=> 2m = 2×9

=> 2m = 18

Also,

=> m² + 1 = 9² + 1

=> m² + 1 = 81 + 1

=> m² + 1 = 82

Hence,

The required Pythagorean triplet is ;

18 , 80 , 82 .