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Pre-Algebra/Expressions,Equations,Integers

Pre-Algebra/Fractions,Percents

Algebra/Exponents,Equations,Radicals

Is there a formula to find all the triples?

Take any two numbers, for example, n and m, and n>m and then find:

n² − m²

n² +m²

For example: Take n=2 m =1 2(1*2) = 4 2 squared = 4 - 1 squared = 4-1 =3 and 2 squared + 1 squared =5 so you have 3,4,5

List of Common Pythagorean Triples

Triple	Triple x2	Triple x 3	Triple x 4
3, 4, 5	6,8,10	9,12,15	12,16,20
5,12,13	10,24,26	15,36,39	20,48,52
7,24,25	14,48,50	21,72,75	28,96,100
8,15,17	16,30,34	24,45,51	32,60,68
9,40,41	18,80,82	27,120,123	36,160,164
11,60,61	22,120,122	33,180,183	44,240,244
12,35,37	24,70,74	36,105,111	48,140,148
13,84,85	26,168,170	39,252,255	52,336,340
16,63,65	32,126,130	48,189,195	64,252,260
20,21,29	40,42,58	60,63,87	80,84,116

Pythagorean Triples are positive integers that satisfy the Pythagorean Theorem, and any multiples of these numbers also fulfill the Pythagorean Theorem.

Take the numbers 3, 4, and 5

3 squared=9 4 squared=16 and 5 squared =25 so 9+16=25 and therefore this triplet of numbers satisfies the Pythagorean Theorem

If you multiply all three numbers by 3 (9, 12, and 15), these new numbers also fulfill the Pythagorean Theorem. 9 squared = 81 12 squared = 144 15 squared =225

81 + 144 =225

Transcript Common Triples

Hi welcome to MooMooMath. Today we are going to look at common triples which are associated with the Pythagorean Theorem. Here is a common triple., a three four five which works in the Pythagorean theorem because 3 squared ( 9 ) plus four squared ( 16 ) equals 5 squared ( 25 16 + 9 equals 25 ) so we have the numbers three. Four and five which are a common triple. In the Pythagorean Theorem. Below it are a triangle with a side of 6 and a hypotenuse of 10 and an X as the unknown side of X if you will notice this shows you a common triple. So three and 6 are associated with each other so they are corresponding sides and if I double 3 I get 6 and if I double 5 I get 10. Therefore if I double 4 I get 8 so the missing side is 8 so this is just applying the Pythagorean Theorem triple to an actual problem. So what are the actual rules for doing this? So what you will do is take your common triplets and multiple each number by the same factor. So we have a three, four, and five and in the example we multiplied each side by two to get a six, eight, ten triangle. You can also go back and multiple 3, 4, 5 by three and get 9, 12. and 15. You get do that with 4 10 or a 40, 50 right triangle. So what are the common triples? Let me show you several of the common triples you will see. 3, 4, 5 and multiples of those. A 5, 12, 13 is also a common triple. Because 5 squared plus 12 squared equals 13 squared. 25 plus 144 equals 169. Here are three more common triples 7, 24, 25 the 8, 15, 17 and the 20, 21, 29. So those are common triples you can take and multiple by sides by common factors. So you can see how this is done. Since I showed you the 3, 4, 5 triple first this time I will use the 5, 12, and 13. So if I were to make a table of possible values I will just draw the 5, 12, and 13 on top and make a list. If I multiple by two I get 10, 24, and 26. And multiple by three I get 15 26, 39 and by 4 I get 20 48 and 52 and those would be our common triples of 5, 12, 13. Hope this was helpful

Pythagorean Triples List

Pythagorean Triplets

What is the formula for Pythagorean Theorem?

a^2 + b^2 = c^2

The square of leg a plus the square of leg b equals the square of the hypotenuse c

Pythagorean Theorem Visually

Pythagorean Theorem Formula