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Question

If the largest number in a Pythagorean triplet is 17, then what is the smallest number in that triplet?
  1. 8
  2. 9
  3. 13
  4. 12


Solution

The correct option is A 8
All the numbers in a Pythagorean triplets are natural numbers and given, the largest number of a Pythagorean triplet is 17.

If one of the other numbers is
a) 13, then the third number will be
172132=120, not a perfect square.

b) 12, then the third number will be
172122=145, not a perfect square.

c) 8, then the third number will be
17282=225=15, a perfect square. 

d) 9, then the third number will be
17292=208, not a perfect square.


Hence, the smallest number in the Pythagorean triplet with the largest number in it as 17, is 8.

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