# Pythagorean triplets explained with examples

Know and learn complete details about Pythagorean triplets. Problems based on Pythagoras theorem can be solved easily if you know Pythagorean triplets.

Every time instead of applying Pythagoras theorem for finding sides of right angled triangle you can make use of this triplets.

First, it is required to know what is Pythagoras theorem. After that, we will study its triplets. Pythagoras theorem definition is given as “For a given any right angled triangle, hypotenuse square will be always equal to the sum of squares of remaining two sides”.

Here, Hypotenuse = RQ and the remaining two sides are PQ and PR.

Therefore, according to Pythagoras theorem statement, we can write it as

${ hypotenuse }^{ 2 }$ = ${ side }^{ 2 }$ + ${ side }^{ 2 }$

${ RQ }^{ 2 }$ = ${ PQ }^{ 2 }$ + ${ PR }^{ 2 }$

## Now we will study about Pythagorean triplets:

The numbers which satisfies Pythagoras theorem are called Pythagorean triplets.

Example:

3, 4, and 5 is one of the important Pythagorean triplets because ${ 5 }^{ 2 }$ = ${ 3 }^{ 2 }$ + ${ 4 }^{ 2 }$, here the greatest number will be always hypotenuse.

### The Formula for finding Pythagorean triplets:

The general notation of Pythagorean triplets is ${ P }^{ 2 }$ – 1, 2P, ${ P }^{ 2 }$ + 1 where P is an integer. 2P represents the least length (side) and ${ P }^{ 2 }$ + 1 represents hypotenuse ${ P }^{ 2 }$ – 1 represents another side of right angled triangle.

Example 1:

If 2P = 8

P = 4

Then ${ P }^{ 2 }$ + 1 = ${ 4 }^{ 2 }$ + 1 = 17

${ P }^{ 2 }$ – 1 = ${ 4 }^{ 2 }$-1 = 15

Therefore, the triplets are 15, 8, 17 because ${ 17 }^{ 2 }$ = ${ 8 }^{ 2 }$ + ${ 15 }^{ 2 }$

Example 2:

If 2P = 14

P = 7

Then ${ P }^{ 2 }$ + 1 = ${ 7 }^{ 2 }$ + 1 = 50

${ P }^{ 2 }$ – 1 = ${ 7 }^{ 2 }$-1 = 48

Therefore, the triplets are 48, 14, 50 because ${ 50 }^{ 2 }$ = ${ 48 }^{ 2 }$ + ${ 14 }^{ 2 }$

#### Some important Pythagorean triplets:

3, 4, 5

8, 6, 10

15, 8, 17

24, 10, 26

35, 12, 37

48, 14, 50

63, 16, 65

80, 18, 82

99, 20, 101

120, 22, 122

143, 24, 145

168, 26, 170

195, 28, 197

224, 30, 226

255, 32, 257

288, 34, 290

323, 36, 325

360, 38, 362

399, 40, 401

440, 42, 442

483, 44, 485

528, 46, 530

575, 48, 577

624, 50, 626

675, 52, 677

728, 54, 730

783, 56, 785

840, 58, 842

899, 60, 901

960, 62, 962

1023, 64, 1025

1088, 66, 1090

1155, 68, 1157

1224, 70, 1226

1295, 72, 1297

1368, 74, 1370

1443, 76, 1445

1520, 78, 1522

1599, 80, 1601

1680, 82, 1682

1763, 84, 1765

1848, 86, 1850

1935, 88, 1937

2024, 90, 2026

2115, 92, 2117

2208, 94, 2210

2303, 96, 2305

2400, 98, 2402

2499, 100, 2501

Note:

Try to remember at least first 5 to 6 triplets