Question

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! (5 points)

Answer 1

Pythagorean triples are sets of numbers that when plugged in to the pythagorean theorem they come out an whole number

7 squared plus 24 squared equals 25 squared
49 plus 576 equals 625
625 equals 625 
This would be a pythagorean triple

9 squared plus 40 squared equals 41 squared
81 plus 1600 equals 1681
1681 equals 1681
This would be a pythagorean triple

Hope this helps :)

Answer 2

Answer:

Check below.

Step-by-step explanation:

The Pitagoras' theorem says that for a right triangle is true that  

$a^2+b^2 = c^2$

where a and b are the legs and c the hypotenuse. Now, a pythagorean triple are three numbers that satisfies that rule. That is, we have that three integers x,y and n are a pytagorean triple if they satisfy that

$x^2+y^2 = n^2$.

For the case of 7,24 and 25:

$7^2 + 24^2 = 49 + 576 = 625$ and $\sqrt{625} = 25$, then $25^2 = 625$, so

$7^2 + 24^2 = 25^2$

For the case of 9, 40 and 41:

$9^2 + 40^2 = 81 + 1600 = 1681$ and $\sqrt{1681} = 41$, then $41^2 = 1681$, so

$9^2 + 40^2 = 41^2$.