Roboguru

Perhatikan gambar berikut. Diketahui , dan . Panjang AB adalah ..

Pertanyaan

Perhatikan gambar berikut.



Diketahui begin mathsize 14px style AC equals 15 space cm comma space EC equals 5 space cm comma space AD equals 6 space cm end style, dan size 14px BC size 14px equals size 14px 3 size 14px space size 14px cm. Panjang AB adalah ..

  1. begin mathsize 14px style 5 square root of 6 end style 

  2. begin mathsize 14px style 6 square root of 5 end style 

  3. begin mathsize 14px style 10 square root of 18 end style 

  4. begin mathsize 14px style 18 square root of 10 end style 

Pembahasan Soal:

Perhatikan segitiga siku-siku BEC!

Gunakan teorema Pythagoras untuk menentukan panjang BE.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell EC squared end cell equals cell BC squared plus BE squared end cell row cell BE squared end cell equals cell EC squared minus BC squared end cell row cell BE squared end cell equals cell 5 squared minus 3 squared end cell row cell BE squared end cell equals cell 25 minus 9 end cell row cell BE squared end cell equals 16 row BE equals cell plus-or-minus square root of 16 end cell row BE equals cell plus-or-minus 4 space cm end cell end table end style 

Karena panjang sisi segitiga tidak mungkin negatif, maka pilih table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px BE end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px cm end table.

Perhatikan segitiga siku-siku EAD!

Karena panjang begin mathsize 14px style AC equals 15 space cm end style, maka panjang AE:

begin mathsize 14px style AC equals AE plus EC AE equals AC minus EC AE equals 15 minus 5 AE equals 10 space cm end style 

Gunakan teorema Pythagoras untuk menentukan panjang ED.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AE squared end cell equals cell AD squared plus ED squared end cell row cell ED squared end cell equals cell AE squared minus AD squared end cell row cell ED squared end cell equals cell 10 squared minus 6 squared end cell row cell ED squared end cell equals cell 100 minus 36 end cell row cell ED squared end cell equals 64 row ED equals cell plus-or-minus square root of 64 end cell row ED equals cell plus-or-minus 8 space cm end cell end table end style 

 Karena panjang sisi segitiga tidak mungkin negatif, maka pilih table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px ED end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 8 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px cm end table.

Perhatikan segitiga siku-siku BAD!

Gunakan teorema Pythagoras untuk menentukan panjang AB.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB squared end cell equals cell AD squared plus BD squared end cell row cell AB squared end cell equals cell AD squared plus open parentheses BE plus ED close parentheses squared end cell row cell AB squared end cell equals cell 6 squared plus open parentheses 4 plus 8 close parentheses squared end cell row cell AB squared end cell equals cell 36 plus 144 end cell row cell AB squared end cell equals 180 row AB equals cell plus-or-minus square root of 180 end cell row AB equals cell plus-or-minus square root of 36 times 5 end root end cell row AB equals cell plus-or-minus 6 square root of 5 space cm end cell end table end style  

Karena panjang sisi segitiga tidak mungkin negatif, maka pilih begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank AB end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 5 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cm end table end style.

Jadi, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 15 Maret 2021

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