Question

This is the most confusing thing I have ever had to do for this class:


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!

Answer 1

Do you know what a Pythagorean triple is?

Answer 2

No, I do not.

Answer 3

Okay, that would make this problem pretty difficult :-)

Answer 4

A Pythagorean triple is a set of 3 numbers which could be the lengths of the sides of a right triangle. As the lengths of the sides of a right triangle, they must obey the Pythagorean theorem, which says that the sum of the squares of the lengths of the two shorter sides equals the square of the length of the longest side.

Answer 5

if you have a right triangle labeled like this, then \[a^2+b^2=c^2\]

Answer 6

So, if you have a set of 3 numbers, if you can substitute them into that formula and get a true statement, they are a Pythagorean triple. The most commonly known one is 3,4,5, because \[3^2 + 4^2 = 5^2\]\[3*3+4*4=5*5\]\[9+16=25\]

Answer 7

ohh i see

Answer 8

1,2,3 is NOT a Pythagorean triple:
\[1^2+2^2=3^2\]\[1*1+2*2=3*3\]\[1+4=9\]\[5=9\]that's not true, so not a Pythagorean triple.

Answer 9

oh

Answer 10

I don't understand what to put for my question

Answer 11

9 would be 3^2

Answer 12

Well, one of the triples is 7, 24, 25. You need to show that \[7^2+24^2 = 25^2\]

Answer 13

so 49 +576 + 625

Answer 14

no, you're missing an = in there

Answer 15

oh my bad

Answer 16

one of the valuable aspects of math class, even if you never need to use the math you learn again, is that it teaches one to work carefully...

Answer 17

yes, my bad