The sets of numbers 7, 24, 25 and 9, 40, 41 are pythagorean triples. use what you know about the pythagorean theorem and explain or show why they are pythagorean triples. be sure to show your work for each set of triples!

By Pythagoras' Theorem:

Sum of the squares of the two side  = Square of longest side

a² + b² = c²

a)

So let's check 7, 24, 25

Is 7² + 24² = 25²  ?

7*7 + 24*24

49 + 576 

=625.

Let us perform the other side 25²

25² = 25 * 25 = 625

Therefore the left hand side = Right hand side.

Therefore 7, 24, 25 is a Pythagorean Triple

b)

Let's check 9, 40, 41

Is 9² + 40² = 41²  ?

9² + 40²

9*9+ 40*40 

81 + 1600

=1681

Let us perform the other side 41²

41² = 41 * 41 = 1681

Therefore the left hand side = Right hand side.

Therefore 9, 40, 41 is a Pythagorean Triple.

The 2 smaller numbers squared equal the larger one

7^2 + 24^2 = 25^2

9^2 + 40^2 = 41^2