Find all pythagorean triples in which one of the three numbe

Find all pythagorean triples in which one of the three numbers is 7. Explain your answer

a^2 + b^2 = c^2

No two perfect squares add to give 7^2

So, c cannot be 7

Let a or b = 7 :

a^2 + 7^2 = c^2

c^2 - a^2 = 49

(c - a)(c + a) = 49

(c - a)(c + a) = 1 * 49

c - a = 1
c + a = 49

Adding , 2c = 50, c = 25
So, a = 24

So, the only pythagorean triple is : (7 , 24 , 25)