Question

Which of the following IS a Pythagorean triple?
a 0.5, 1.2, 1.5
b 0.3, 0.4, 0.7
c 10, 24, 26
d 7, 9, 13

Which of the following is NOT a Pythagorean triple?
a 0.5, 1.2, 1.3
b 6, 8, 10
c 3, 4, 5
d 1, 2, 3Which of the following IS a Pythagorean triple?
a 0.5, 1.2, 1.5
b 0.3, 0.4, 0.7
c 10, 24, 26
d 7, 9, 13

Which of the following is NOT a Pythagorean triple?
a 0.5, 1.2, 1.3
b 6, 8, 10
c 3, 4, 5
d 1, 2, 3

Answer 1

well p-triples need to be integers, so on the first one, we know its either c, or d.
100^2+24^2 = 676 = 26^2

Answer 2

that should say 10^2

Answer 3

and since they need to be integers, we know A is the answer to number 2.

Answer 4

understand @nikakuz ?

Answer 5

A Pythagorean triple is a triple that satisfies the Pythagorean Theorem. The formula that has to be satisfied is \[a^2+b^2=c^2\] So you can set the values for each triple and see if the equality is valid. If it is, the triple is a Pythagorean triple. If the equality is invalid, the triple is not a Pythagorean triple. For example: a=0.5, b=1.2, c=1.5
\[0.5^2 + 1.2^2 = 1.5^2\]
\[0.25+1.44=2.25\]
The equality is not valid, so the first triple is not a Pythagorean triple. You can use the same method for the rest.

Answer 6

the need to be integers by definition

Answer 7

@giolefpatceid

Answer 8

ahh I don't get it

Answer 9

do you know what an integer is?

Answer 10

do you see why on the first question choices a and b are not integers?

Answer 11

yes a whole number right?

Answer 12

...-2,-1,0,1,2...

Answer 13

and actually they must be positive integer, so natural numbers
1,2,3,4,5....

Answer 14

ok so that rules out a,b on question 1 right?

Answer 15

yes

Answer 16

then what?

Answer 17

so we have
ok so we need to check 10, 24, 26
a Pythagorean triples is 3 positive integers such that if you take the two smaller numbers 10,24 and square them 10^2 = 100 and 24^2 = 576, then add them 576+100 = 676 and then take the positive square root of that sqrt(676) = the bigger number = 26, and thus 10,24,26 is a Pythagorean triple.

Answer 18

so
\[10^{2}+24^{2} = 26^{2}\]

Answer 19

Thank you!!!!

Answer 20

so knowing that Pythagorean triples need to be integers, what is the answer to part 2?

Answer 21

a right?

Answer 22

yep

Answer 23

Thanks!!! :)

Answer 24

np

Answer 25

just a note: I have seen others ask question about Pythagorean triples in here, and the only answers their book gave were decimals. There are decimals that satisfy this property a^2 + b^2 = c^2, where a,b,and c are decimals. But if you google the definition of a Pythagorean triples you will see it says integers. having said that, most people are not in a number theory class, and since this is just basic algebra, the book you are using might not take into account that they need to be integers. You may want to ask your teacher. If anything he/she will be stokes you asked:)

Answer 26

stoked*

Answer 27

that's 90's talk for happy...