Question

in the following identify the Pythagorean triplet(12,35,37)

Answer 1

for Pythagorean triplet
a^2+ b^2 =c^2
take a as 12 , b as 35 and c as 37
now
12*12 + 35*35=37*37
144 + 1225= 1369
1369 = 1369
hence
it is proved that 12 35 and 37 are in Pythagorean triplet

Answer 2

Let,
a=12(even)
b=35
c=37
Case I,
If a is even sum of other two numbers is a^2/2.
So, b+c=35+37=72
$\frac{a {}^{2} }{2} = \frac{12 {}^{2} }{2} = \frac{144}{2} = 72$
First case verified.

Case ll,
If a is even difference of other two numbers is 2.
So, c-b=37-35=2
Second Case verified.


So, both cases are verified.
Hence, (12,35,37) is a Pythagorean triplet.