Which set of numbers could represent the length of the sides of a right triangle?

Comment

You can generate as many of these as you like by using this relationship

a = x^2 - y^2

b = 2xy

c = x^2 + y^2

Examples

x = 2 y = 1

a^2 + b^2 = c^2

a = 2^2 - 1^2

a = 4 - 1

a = 3

b = 2*2*1

b = 4

c = 2^2 + 1^2

c = 4 + 1

c = 5

So now you have a familiar example, the 3, 4, 5 triangle.

Check it

a^2 + b^2 = c^2

3^2 + 4^2 = 5^2

9 + 16 = 25

25 = 25

Another example (a little more complicated)

x = 7

y = 2

a = 7^2 - 2^2

a = 49 - 4

a = 45

b = 2xy

b = 2*7*2

b = 28

c = 7^2 + 2^2

c = 49 + 4

c = 53 This one is not well known.

a^2 + b^2 = c^2

45^2 + 28^2 = 53^2

2025 + 784 = ? 2809

2809 = 2809

So this one is also a right angle triangle.

You cannot find a counterexample which will make this procedure untrue. Nice to have in your math kitbag.