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Pada layang-layang ABCD di samping, panjang begin mathsize 14px style AD equals 20 space cm comma space OD equals 16 space cm end style, dan size 14px AC size 14px equals size 14px 42 size 14px space size 14px cm.

a. Hitunglah panjang OA, OC, dan BC!

b. Hitunglah keliling layang-layang ABCD tersebut!

A. Acfreelance

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

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Jawaban

keliling layang-layang ABCD adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 86 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.

Pembahasan

Diketahui panjang begin mathsize 14px style AD equals 20 space cm comma space OD equals 16 space cm end style, dan size 14px AC size 14px equals size 14px 42 size 14px space size 14px cm

Perhatikan segitiga AOD!

Karena segitiga AOD adalah segitiga siku-siku, maka gunakan teorema Pythagoras untuk menentukan panjang OA.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AD squared end cell equals cell OA squared plus OD squared end cell row cell OA squared end cell equals cell AD squared plus OD squared end cell row cell OA squared end cell equals cell 20 squared plus 16 squared end cell row cell OA squared end cell equals cell 400 plus 256 end cell row cell OA squared end cell equals 656 row OA equals cell plus-or-minus square root of 656 end cell row OA equals cell plus-or-minus 25 comma 6 space cm end cell end table end style 

  

Panjang sisi layang-layang tidak mungkin negatif, maka pilih begin mathsize 14px style OA equals 25 comma 6 space cm end style.

Sehingga, panjang OC:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row AC equals cell OA plus OC end cell row OC equals cell AC minus OA end cell row OC equals cell 42 minus 25 comma 6 end cell row OC equals cell 16 comma 4 space cm end cell end table end style

Perhatikan segitiga DOC!

Karena segitiga DOC adalah segitiga siku-siku, maka gunakan teorema Pythagoras untuk menentukan panjang DC.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell DC squared end cell equals cell OC squared plus OD squared end cell row cell DC squared end cell equals cell 16 comma 4 squared plus 16 squared end cell row cell DC squared end cell equals cell 268 comma 96 plus 256 end cell row cell DC squared end cell equals cell 524 comma 96 end cell row cell DC squared end cell equals cell plus-or-minus square root of 524 comma 96 end root end cell row DC equals cell plus-or-minus 22 comma 9 space cm end cell row DC almost equal to cell plus-or-minus 23 space cm end cell end table end style   

Panjang sisi layang-layang tidak mungkin negatif, maka pilih begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank DC 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 23 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.

Layang-layang mempunyai 2 pasang sisi sama panjang yaitu begin mathsize 14px style AB equals AD end style dan size 14px BC size 14px equals size 14px DC. Sehingga panjang BC adalah begin mathsize 14px style 23 space cm end style.

Maka, keliling layang-layang:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight K equals cell 2 left parenthesis AD plus DC right parenthesis end cell row blank equals cell 2 times left parenthesis 20 plus 23 right parenthesis end cell row blank equals cell 2 times 43 end cell row blank equals cell 86 space cm end cell end table end style  

Jadi, keliling layang-layang ABCD adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 86 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.

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