Pertanyaan

Hitunglah panjang sisi yang diberi label pada gambar di bawah ini. (semua dalam satuan sentimeter)

Hitunglah panjang sisi yang diberi label pada gambar

di bawah ini. (semua dalam satuan sentimeter)

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Jawaban terverifikasi

Pembahasan

Gambar 1 Nilai a, Jadi, nilai a adalah 6,43 cm nilai b, Jadi, panjang b adalah 12.86 cm Gambar 2 Substitusi nilai df, Jadi, panjang d adalah 7 cm Jadi, panjang f adalah cm Jadi, panjang nilai e adalah 10 cm Jadi, panjang c adalah 5 cm Gambar 3 nilai p, Jadi, nilai p adalah 4 cm Panjang BC nilai q, Jadi, nilai q adalah 8 cm Gambar 4 Nilai x, Jadi, panjang x adalah 25,2 cm nilai y, Jadi, panjang y adalah 28,8 cm nilai z, Jadi, panjang z adalah 9,6 cm

Gambar 1

$triangle P S T almost equal to triangle P Q R fraction numerator P S over denominator P Q end fraction equals fraction numerator P T over denominator P R end fraction equals fraction numerator S T over denominator Q R end fraction$

Nilai a,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator P S over denominator P Q end fraction end cell equals cell fraction numerator P T over denominator P R end fraction end cell row cell a over 15 end cell equals cell 9 over 21 end cell row cell a times 21 end cell equals cell 9 times 15 end cell row cell 21 a end cell equals 135 row a equals cell 6 comma 43 space cm end cell end table$

Jadi, nilai a adalah 6,43 cm

nilai b,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator P T over denominator P R end fraction end cell equals cell fraction numerator S T over denominator Q R end fraction end cell row cell 9 over 21 end cell equals cell b over 30 end cell row cell b times 21 end cell equals cell 9 times 30 end cell row cell 21 b end cell equals 270 row b equals cell 12 comma 86 space cm end cell end table$

Jadi, panjang b adalah 12.86 cm

Gambar 2

$triangle M Q N almost equal to triangle L Q R fraction numerator Q R over denominator Q M end fraction equals fraction numerator Q L over denominator Q N end fraction equals fraction numerator L R over denominator M N end fraction$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator Q R over denominator Q M end fraction end cell equals cell fraction numerator L R over denominator M N end fraction end cell row cell 5 over d end cell equals cell f over 12 end cell row cell f times d end cell equals cell 5 times 12 end cell row cell d f end cell equals 60 row blank blank blank end table$

Substitusi nilai df,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator P Q over denominator L R end fraction end cell equals cell fraction numerator M Q over denominator M R end fraction end cell row cell 5 over f end cell equals cell fraction numerator d over denominator 5 plus d end fraction end cell row cell d f end cell equals cell 5 left parenthesis 5 plus d right parenthesis end cell row 60 equals cell 25 plus 5 d end cell row 35 equals cell 5 d end cell row d equals cell 7 space cm end cell end table$

Jadi, panjang d adalah 7 cm

table attributes columnalign right center left columnspacing 0px end attributes row cell d f end cell equals 60 row cell 7 f end cell equals 60 row f equals cell 60 over 7 cm end cell end table

Jadi, panjang f adalah cm

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator Q L over denominator Q N end fraction end cell equals cell fraction numerator L R over denominator M N end fraction end cell row cell e over 14 end cell equals cell fraction numerator 60 over 7 over denominator 12 end fraction end cell row cell 12 times e end cell equals cell 60 over 7 times 14 end cell row cell 12 e end cell equals cell 60 times 2 end cell row cell 12 e end cell equals 120 row e equals cell 10 space cm end cell end table$

Jadi, panjang nilai e adalah 10 cm

$triangle M P Q almost equal to triangle M L R fraction numerator M P over denominator M L end fraction equals fraction numerator P Q over denominator L R end fraction equals fraction numerator M Q over denominator M R end fraction$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator M P over denominator M L end fraction end cell equals cell fraction numerator M Q over denominator M R end fraction end cell row cell fraction numerator 7 over denominator 7 plus c end fraction end cell equals cell 7 over 12 end cell row cell 7 left parenthesis 7 plus c right parenthesis end cell equals cell 7 times 12 end cell row cell 49 plus 7 c end cell equals 84 row cell 7 c end cell equals 35 row c equals cell 5 space cm end cell end table$

Jadi, panjang c adalah 5 cm

Gambar 3

$triangle A B C almost equal to triangle E F C fraction numerator A B over denominator E F end fraction equals fraction numerator C B over denominator C F end fraction equals fraction numerator A C over denominator C E end fraction$

nilai p,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator A B over denominator E F end fraction end cell equals cell fraction numerator C B over denominator C F end fraction end cell row cell 9 over 6 end cell equals cell fraction numerator 8 plus p over denominator 8 end fraction end cell row cell 6 left parenthesis 8 plus p right parenthesis end cell equals cell 9 times 8 end cell row cell 48 plus 6 p end cell equals 72 row cell 6 p end cell equals 24 row p equals cell 4 space cm end cell end table$

Jadi, nilai p adalah 4 cm

Panjang BC

table attributes columnalign right center left columnspacing 0px end attributes row cell B C end cell equals cell B F plus F C end cell row blank equals cell 8 plus 4 end cell row blank equals 12 end table

$triangle D B C almost equal to triangle G B F fraction numerator B D over denominator B G end fraction equals fraction numerator D C over denominator G F end fraction equals fraction numerator B C over denominator B F end fraction$

nilai q,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator D C over denominator G F end fraction end cell equals cell fraction numerator B C over denominator B F end fraction end cell row cell 24 over q end cell equals cell 12 over 4 end cell row cell 12 times q end cell equals cell 24 times 4 end cell row cell 12 q end cell equals 96 row q equals cell 8 space cm end cell end table$

Jadi, nilai q adalah 8 cm

Gambar 4

$triangle S O T almost equal to triangle Q O R fraction numerator S O over denominator O R end fraction equals fraction numerator T O over denominator O Q end fraction equals fraction numerator S T over denominator Q R end fraction$

Nilai x,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator S O over denominator O R end fraction end cell equals cell fraction numerator T O over denominator O Q end fraction end cell row cell 10 over 18 end cell equals cell 14 over x end cell row cell 10 times x end cell equals cell 14 times 18 end cell row cell 10 x end cell equals 252 row x equals cell 25 comma 2 space cm end cell end table$

Jadi, panjang x adalah 25,2 cm

nilai y,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator S O over denominator O R end fraction end cell equals cell fraction numerator S T over denominator Q R end fraction end cell row cell 10 over 18 end cell equals cell 16 over y end cell row cell 10 times y end cell equals cell 16 times 18 end cell row cell 10 y end cell equals 288 row y equals cell 28 comma 8 space cm end cell end table$

Jadi, panjang y adalah 28,8 cm

nilai z,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator S T over denominator Q R end fraction end cell equals cell fraction numerator S P over denominator Q P end fraction end cell row cell fraction numerator 16 over denominator 28 comma 8 end fraction end cell equals cell fraction numerator 12 over denominator 12 plus z end fraction end cell row cell 16 left parenthesis 12 plus z right parenthesis end cell equals cell 12 times 28 comma 8 end cell row cell 192 plus 16 z end cell equals cell 345 comma 6 end cell row cell 16 z end cell equals cell 153 comma 6 end cell row z equals cell 9 comma 6 space cm end cell end table$

Jadi, panjang z adalah 9,6 cm