Pythagorean Triple?

Question

The set of intergerst {5,12,13,} is an example of a Pythagorean triple. Which if the following is another example example?


{6,9,12}
{7,24,25}
{7,12,13}
{7,8,9}



how can i figure this out?

Answer 1

7 24 25

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime.

The name is derived from the Pythagorean theorem, of which every Pythagorean triple is a solution. The converse is not true. For instance, the triangle with sides a = b = 1 and c = √2 is right, but (1, 1, √2) is not a Pythagorean triple because √2 is not an integer. Moreover, 1 and √2 don't have an integer common multiple because √2 is irrational. There are 16 primitive Pythagorean triples with c ≤ 100:

(3, 4, 5) (20, 21, 29) (11, 60, 61) (13, 84, 85)
(5, 12, 13) (12, 35, 37) (16, 63, 65) (36, 77, 85)
(8, 15, 17) (9, 40, 41) (33, 56, 65) (39, 80, 89)
(7, 24, 25) (28, 45, 53) (48, 55, 73) (65, 72, 97)

Answer 2

Suppose that m and n are two positive integers, with m < n. Then n2 - m2, 2mn, and n2 + m2 is a Pythagorean triple.

It's easy to check algebraically that the sum of the squares of the first two is the same as the square of the last one

in the example that you have
5*5=25 12*12=144 25+144=169 13*13=169

Answer 3

A Pythagorean triple is a set of three numbers in which the smaller two squared then added up equals the biggest one squared. (Like the Pythagorean theorem.)

For {5,12,13}, 5² + 12² = 13²

Try this with the rest and figure out which one fits the pattern.

Answer 4

well, it can't be 7,12,13 since we know that 5 goes with 12 and 13.

Here's the easy method. Square the small number, and add the two big numbers. If those are the same, then it's a pythagorean triple

7² = 49
24 + 25 = 49

7, 24, 25 is a pythagorean triple.

Answer 5

{7,24,25}
Because 7^2 + 24^2 = 25^2

(just like 5^2 + 12^2 = 13^2)

Answer 6

well if you know the pythogorean therum it can be quite easy
lets take the intergers in the example
5^2+12^2=13^2
then find out if that is correct
25+144=169
169=169
that's correct so i'll do the next part for you

the answer is {7,24,25}
because
7^2+24^2=25^2

Answer 7

See if x^2 + y^2 = z^2 for each set of 3 numbers.

Done.