Question

If the largest number in a Pythagorean triplet is 17, then what is the smallest number in that triplet?

• A. 13
• B. 12
• C. 8
• D. 9

Answer 1

The correct option is C 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
$\sqrt{{17}^2-{13}^2}=\sqrt{120}\text{, not a perfect square.}$

b) 12, then the third number will be
$\sqrt{{17}^2-{12}^2}=\sqrt{145}\text{, not a perfect square.}$

c) 8, then the third number will be
$\sqrt{{17}^2-8^2}=\sqrt{225}=15\text{, a perfect square.}$

d) 9, then the third number will be
$\sqrt{{17}^2-9^2}=\sqrt{208}\text{, not a perfect square.}$


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