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Lengkapi tabel untuk mengecek apakah bilangan-bilangan berikut merupakan tripel Pythagoras!

Pertanyaan

Lengkapi tabel untuk mengecek apakah bilangan-bilangan berikut merupakan tripel Pythagoras!

Pembahasan Soal:

Triple Pythagoras adalah tiga bilangan bulat positif begin mathsize 14px style a end style, begin mathsize 14px style b end style, dan begin mathsize 14px style straight c end style yang memenuhi Teorema Pythagoras. Berbunyi "Kuadrat bilangan terbesar merupakan jumlah kuadrat dua bilangan lainnya" yaitu begin mathsize 14px style a squared plus b squared equals c squared end style, dengan begin mathsize 14px style straight c end style merupakan bilangan terbesar.

Didapat bahwa:

  • Bilangan begin mathsize 14px style a equals 3 end stylebegin mathsize 14px style b equals 4 end style, dan begin mathsize 14px style c equals 6 end style.

dengan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell 3 squared plus 4 squared end cell row blank equals cell 9 plus 16 end cell row blank equals 25 end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared end cell equals cell 6 squared end cell row blank equals 36 end table end style

Karena begin mathsize 14px style 3 comma space 4 comma space 6 end style tidak memenuhi begin mathsize 14px style a squared plus b squared equals c squared end style atau begin mathsize 14px style 3 squared plus 4 squared not equal to 6 squared end style, maka bilangan begin mathsize 14px style 3 comma space 4 comma space 6 end style bukan Tripel Pythagoras.

 

  • Bilangan begin mathsize 14px style a equals 6 end stylebegin mathsize 14px style b equals 8 end style, dan begin mathsize 14px style c equals 10 end style.

dengan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell 6 squared plus 8 squared end cell row blank equals cell 36 plus 64 end cell row blank equals 100 end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared end cell equals cell 10 squared end cell row blank equals 100 end table end style

Karena begin mathsize 14px style 6 comma space 8 comma space 10 end style memenuhi begin mathsize 14px style a squared plus b squared equals c squared end style atau begin mathsize 14px style 6 squared plus 8 squared equals 10 squared end style, maka bilangan begin mathsize 14px style 6 comma space 8 comma space 10 end style Tripel Pythagoras.

 

  • Bilangan begin mathsize 14px style a equals 9 end stylebegin mathsize 14px style b equals 12 end style, dan begin mathsize 14px style c equals 15 end style.

dengan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell 9 squared plus 12 squared end cell row blank equals cell 81 plus 144 end cell row blank equals 225 end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared end cell equals cell 15 squared end cell row blank equals 225 end table end style

Karena begin mathsize 14px style 9 comma space 12 comma space 15 end style memenuhi begin mathsize 14px style a squared plus b squared equals c squared end style atau begin mathsize 14px style 9 squared plus 12 squared equals 15 squared end style, maka bilangan begin mathsize 14px style 9 comma space 12 comma space 15 end style Tripel Pythagoras.

 

  • Bilangan begin mathsize 14px style a equals 12 end stylebegin mathsize 14px style b equals 16 space cm end style, dan begin mathsize 14px style c equals 20 end style.

dengan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell 12 squared plus 16 squared end cell row blank equals cell 144 plus 256 end cell row blank equals 400 end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared end cell equals cell 20 squared end cell row blank equals 400 end table end style

Karena begin mathsize 14px style 12 comma space 16 comma space 20 end style memenuhi begin mathsize 14px style a squared plus b squared equals c squared end style atau begin mathsize 14px style 12 squared plus 16 squared equals 20 squared end style, maka bilangan begin mathsize 14px style 12 comma space 16 comma space 20 end style Tripel Pythagoras.

 

  • Bilangan begin mathsize 14px style a equals 5 end styleundefined, dan begin mathsize 14px style c equals 13 end style.

dengan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell 5 squared plus 12 squared end cell row blank equals cell 25 plus 144 end cell row blank equals 169 end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared end cell equals cell 13 squared end cell row blank equals 169 end table end style

Karena begin mathsize 14px style 5 comma space 12 comma space 13 end style memenuhi begin mathsize 14px style a squared plus b squared equals c squared end style atau begin mathsize 14px style 5 squared plus 12 squared equals 13 squared end style, maka bilangan begin mathsize 14px style 5 comma space 12 comma space 13 end style Tripel Pythagoras.

 

  • Bilangan begin mathsize 14px style a equals 10 end stylebegin mathsize 14px style b equals 24 end style, dan undefined.

dengan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell 10 squared plus 24 squared end cell row blank equals cell 100 plus 576 end cell row blank equals 676 end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared end cell equals cell 25 squared end cell row blank equals 625 end table end style

Karena begin mathsize 14px style 10 comma space 24 comma space 25 end style tidak memenuhi begin mathsize 14px style a squared plus b squared equals c squared end style atau begin mathsize 14px style 10 squared plus 24 squared not equal to 25 squared end style, maka bilangan begin mathsize 14px style 10 comma space 24 comma space 25 end style bukan Tripel Pythagoras.

 

  • Bilangan begin mathsize 14px style a equals 7 end styleundefined, dan undefined.

dengan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell 7 squared plus 24 squared end cell row blank equals cell 49 plus 576 end cell row blank equals 625 end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight c squared end cell equals cell 25 squared end cell row blank equals 625 end table end style

Karena begin mathsize 14px style 7 comma space 24 comma space 25 end style memenuhi begin mathsize 14px style a squared plus b squared equals c squared end style atau begin mathsize 14px style 7 squared plus 24 squared equals 25 squared end style, maka bilangan begin mathsize 14px style 7 comma space 24 comma space 25 end style Tripel Pythagoras.

 

  • Bilangan begin mathsize 14px style a equals 14 end stylebegin mathsize 14px style b equals 48 end style, dan begin mathsize 14px style c equals 52 end style.

dengan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell 14 squared plus 48 squared end cell row blank equals cell 196 plus 2.304 end cell row blank equals cell 2.500 end cell end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared end cell equals cell 52 squared end cell row blank equals cell 2.704 end cell end table end style

Karena begin mathsize 14px style 14 comma space 48 comma space 52 end style tidak memenuhi begin mathsize 14px style a squared plus b squared equals c squared end style atau begin mathsize 14px style 14 squared plus 48 squared not equal to 52 squared end style, maka bilangan begin mathsize 14px style 14 comma space 48 comma space 52 end style bukan Tripel Pythagoras.

 

  • Bilangan begin mathsize 14px style a equals 8 end stylebegin mathsize 14px style b equals 15 end style, dan begin mathsize 14px style c equals 17 end style.

dengan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell 8 squared plus 15 squared end cell row blank equals cell 64 plus 225 end cell row blank equals 289 end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared end cell equals cell 17 squared end cell row blank equals 289 end table end style

Karena begin mathsize 14px style 8 comma space 15 comma space 17 end style memenuhi begin mathsize 14px style a squared plus b squared equals c squared end style atau begin mathsize 14px style 8 squared plus 15 squared equals 17 squared end style, maka bilangan begin mathsize 14px style 8 comma space 15 comma space 17 end style Tripel Pythagoras.

 

  • Bilangan begin mathsize 14px style a equals 16 end stylebegin mathsize 14px style b equals 30 end style, dan begin mathsize 14px style c equals 32 end style.

dengan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell 16 squared plus 30 squared end cell row blank equals cell 256 plus 900 end cell row blank equals cell 1.156 end cell end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared end cell equals cell 32 squared end cell row blank equals cell 1.024 end cell end table end style

Karena begin mathsize 14px style 16 comma space 30 comma space 32 end style tidak memenuhi begin mathsize 14px style a squared plus b squared equals c squared end style atau begin mathsize 14px style 16 squared plus 30 squared not equal to 32 squared end style, maka bilangan begin mathsize 14px style 16 comma space 30 comma space 32 end style bukan Tripel Pythagoras.

 

Digambarkan dalam tabel seperti berikut:

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 April 2021

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