Perhatikan gambar segitiga siku-siku ABC di bawah ini. Tentukan: a. keliling segitiga ABC, b. luas segitiga ABC.

Pertanyaan

Perhatikan gambar segitiga siku-siku ABC di bawah ini.

Tentukan:

a. keliling segitiga ABC,

b. luas segitiga ABC.

... $space$
... $undefined$

Pembahasan Video:

Pembahasan Soal:

Diketahui:

$begin mathsize 14px style AD equals 8 space cm end style$

Perhatikan $begin mathsize 14px style increment ADC space end style$ siku-siku di $begin mathsize 14px style straight D comma end style$ $begin mathsize 14px style angle ACD equals angle CBD equals 30 degree end style$ , maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell angle CAD end cell equals cell 90 degree minus angle ACD end cell row blank equals cell 90 degree minus 30 degree end cell row blank equals cell 60 degree end cell end table end style$

Perbandingan $begin mathsize 14px style AC colon AD end style$ adalah $begin mathsize 14px style 2 colon 1 end style$ , maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AC colon AD end cell equals cell 2 colon 1 space end cell row cell AC over AD end cell equals cell 2 over 1 space end cell row cell AC over 8 end cell equals cell 2 over 1 space end cell row cell AC cross times 1 end cell equals cell 2 cross times 8 space end cell row AC equals cell 16 space cm end cell end table end style$

Perbandingan $begin mathsize 14px style AD colon CD end style$ adalah $begin mathsize 14px style 1 colon square root of 3 end style$ , maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AD colon CD end cell equals cell 1 colon square root of 3 end cell row cell AD over CD end cell equals cell fraction numerator 1 over denominator square root of 3 end fraction end cell row cell 8 over CD end cell equals cell fraction numerator 1 over denominator square root of 3 end fraction end cell row cell 1 cross times CD end cell equals cell 8 cross times square root of 3 end cell row CD equals cell 8 square root of 3 space cm end cell end table end style$

Perhatikan $begin mathsize 14px style ΔBDC end style$ siku-siku di $begin mathsize 14px style straight D comma end style$ $begin mathsize 14px style angle CBD equals 30 degree end style$ , maka:

$undefined$

Perbandingan $begin mathsize 14px style CD colon BD end style$ adalah $begin mathsize 14px style 1 colon square root of 3 end style$ , maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell CD colon BD end cell equals cell 1 colon square root of 3 end cell row cell CD over BD end cell equals cell fraction numerator 1 over denominator square root of 3 end fraction end cell row cell fraction numerator 8 square root of 3 over denominator BD end fraction end cell equals cell fraction numerator 1 over denominator square root of 3 end fraction end cell row cell 1 cross times BD end cell equals cell 8 square root of 3 cross times square root of 3 end cell row BD equals cell 8 square root of 9 end cell row blank equals cell 8 cross times 3 end cell row blank equals cell 24 space cm end cell end table end style$

Perbandingan $begin mathsize 14px style CD colon BC end style$ adalah $begin mathsize 14px style 1 colon 2 end style$ , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px CD size 14px colon size 14px BC end cell size 14px equals cell size 14px 1 size 14px colon size 14px 2 size 14px space end cell row cell size 14px CD over size 14px BC end cell size 14px equals cell size 14px 1 over size 14px 2 end cell row cell fraction numerator size 14px 8 square root of size 14px 3 over denominator size 14px BC end fraction end cell size 14px equals cell size 14px 1 over size 14px 2 end cell row cell size 14px 1 size 14px cross times size 14px BC end cell size 14px equals cell size 14px space size 14px 8 square root of size 14px 3 size 14px cross times size 14px 2 end cell row size 14px BC size 14px equals cell size 14px space size 14px 16 square root of size 14px 3 size 14px space size 14px cm end cell end table$

Sehingga:

a. Keliling segitiga $begin mathsize 14px style ABC end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row K equals cell AD plus BD plus BC plus AC end cell row blank equals cell 8 plus 24 plus 16 square root of 3 plus 16 end cell row blank equals cell 48 plus 16 square root of 3 end cell end table end style$

Kemudian hasilnya kita sederhanakan dengan cara kedua suku dibagi $begin mathsize 14px style 16 end style$ , menjadi:

$begin mathsize 14px style 48 plus 16 square root of 3 equals 16 left parenthesis 3 plus square root of 3 right parenthesis end root end style$

Jadi, keliling segitiga $undefined$ adalah $begin mathsize 14px style 16 left parenthesis 3 plus square root of 3 right parenthesis space cm. end style$

b. Luas segitiga $undefined$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row L equals cell 1 half cross times AB cross times CD end cell row blank equals cell 1 half cross times left parenthesis AD plus BD right parenthesis cross times CD end cell row blank equals cell 1 half cross times left parenthesis 8 plus 24 right parenthesis cross times left parenthesis 8 square root of 3 right parenthesis end cell row blank equals cell 1 half cross times 32 cross times 8 square root of 3 end cell row blank equals cell 128 square root of 3 space cm end cell end table end style$

Jadi, luas segitiga $undefined$ adalah $begin mathsize 14px style 128 square root of 3 space cm. end style$

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 05 Mei 2021

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