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Perhatikan Gambar 5.35! Jika diketahui AD = 2 5 ​ cm dan BD = 4 cm . Tentukan: a. CD; b. BC; c. AB; d. AC!

Perhatikan Gambar 5.35!



 

Jika diketahui  dan . Tentukan:

a. CD;

b. BC;

c. AB;

d. AC!

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A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

panjang ACadalah .

panjang AC adalah begin mathsize 14px style 2 square root of 5 open parentheses 1 plus 4 over 5 close parentheses space cm end style.

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Pembahasan

Perhatikan gambar segitiga siku-siku berikut! Berdasarkan gambar di atas berlaku: Sehingga, a. Sehingga, panjang CD adalah . b. Karena panjang BC tidak mungkin negatif, maka pilih . Sehingga, panjang BCadalah . c. Karena panjang BA tidak mungkin negatif, maka pilih . , makapanjang ABadalah . d. Jadi, panjang ACadalah .

Perhatikan gambar segitiga siku-siku berikut!



 

Berdasarkan gambar di atas berlaku:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB squared end cell equals cell BD cross times BC end cell row cell AC squared end cell equals cell CD cross times CB end cell row cell AD squared end cell equals cell BD cross times CD end cell end table end style 

Sehingga,

a. 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell BD squared end cell equals cell CD times AD end cell row CD equals cell BD squared over AD end cell row CD equals cell fraction numerator 4 squared over denominator 2 square root of 5 end fraction end cell row CD equals cell fraction numerator 16 over denominator 2 square root of 5 end fraction end cell row CD equals cell fraction numerator 8 over denominator square root of 5 end fraction times fraction numerator square root of 5 over denominator square root of 5 end fraction end cell row CD equals cell 8 over 5 square root of 5 space cm end cell end table end style 

Sehingga, panjang CD adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 8 over 5 end cell 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.

b.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell BC squared end cell equals cell CD times CA end cell row cell BC squared end cell equals cell CD times open parentheses CD plus AD close parentheses end cell row cell BC squared end cell equals cell 8 over 5 square root of 5 open parentheses 8 over 5 square root of 5 plus 2 square root of 5 close parentheses end cell row cell BC squared end cell equals cell fraction numerator 64 times 5 over denominator 25 end fraction plus fraction numerator 16 times 5 over denominator 5 end fraction end cell row cell BC squared end cell equals cell fraction numerator 320 plus 400 over denominator 25 end fraction end cell row BC equals cell plus-or-minus square root of 720 over 25 end root end cell row BC equals cell plus-or-minus fraction numerator square root of 144 times 5 end root over denominator square root of 25 end fraction end cell row BC equals cell plus-or-minus 12 over 5 square root of 5 space cm end cell end table end style 

Karena panjang BC tidak mungkin negatif, maka pilih begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank BC 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 cell 12 over 5 end cell 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.

Sehingga, panjang BC adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 12 over 5 end cell 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.

c.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell BA squared end cell equals cell AD times AC end cell row cell BA squared end cell equals cell AD times open parentheses AD plus CD close parentheses end cell row cell BA squared end cell equals cell 2 square root of 5 open parentheses 2 square root of 5 plus 8 over 5 square root of 5 close parentheses end cell row cell BA squared end cell equals cell 4 times 5 plus fraction numerator 16 times 5 over denominator 5 end fraction end cell row cell BA squared end cell equals cell fraction numerator 100 plus 80 over denominator 5 end fraction end cell row BA equals cell plus-or-minus square root of 180 over 5 end root end cell row BA equals cell plus-or-minus fraction numerator square root of 36 times square root of 5 over denominator square root of 5 end fraction end cell row BA equals cell plus-or-minus 6 space cm end cell end table end style 

Karena panjang BA tidak mungkin negatif, maka pilih begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank BA 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 space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cm end table end style.

begin mathsize 14px style AB equals BA end style, maka panjang AB adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 6 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.

d.

begin mathsize 14px style AC equals AD plus CD AC equals 2 square root of 5 plus 8 over 5 square root of 5 AC equals 2 square root of 5 open parentheses 1 plus 4 over 5 close parentheses space cm end style 

Jadi, panjang AC adalah begin mathsize 14px style 2 square root of 5 open parentheses 1 plus 4 over 5 close parentheses space cm end style.

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