Perhatikan gambar berikut! Dari gambar diatas, hitung panjang sisi PQ!

Pertanyaan

Perhatikan gambar berikut!

Dari gambar diatas, hitung panjang sisi PQ!

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Perhatikan segitiga PRS yang siku-siku di titik S.

Ingatlah bahwa jumlah sudut pada segitiga adalah 180 degree.

Sehingga besar sudut R, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell angle straight P plus angle straight R plus angle straight S end cell equals cell 180 degree end cell row cell 30 degree plus angle straight R plus 90 degree end cell equals cell 180 degree end cell row cell 120 degree plus angle straight R end cell equals cell 180 degree end cell row cell angle straight R end cell equals cell 180 degree minus 120 degree end cell row cell angle straight R end cell equals cell 60 degree end cell end table

Kemudian, gunakan rumus oerbandingan sisi pada segitiga siku-siku sudut 30 degree dan 90 degree.

Dengan rumus:

30 degree space colon space 60 degree space colon space 90 degree equals 1 space space colon square root of 3 space colon space 2

Sehingga diperoleh:

  • Panjang PS

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sisi space didepan space 60 degree over denominator sisi space didepan space 90 degree end fraction end cell equals cell fraction numerator square root of 3 over denominator 2 end fraction end cell row cell PS over PR end cell equals cell fraction numerator square root of 3 over denominator 2 end fraction end cell row cell fraction numerator PS over denominator 24 space cm end fraction end cell equals cell fraction numerator square root of 3 over denominator 2 end fraction end cell row cell 2 PS end cell equals cell 24 square root of 3 space cm end cell row PS equals cell fraction numerator 24 square root of 3 space cm over denominator 2 end fraction end cell row PS equals cell 12 square root of 3 space cm end cell end table

  • Panjang RS

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sisi space didepan space 30 degree over denominator sisi space didepan space 90 degree end fraction end cell equals cell 1 half end cell row cell RS over PR end cell equals cell 1 half end cell row cell fraction numerator RS over denominator 24 space cm end fraction end cell equals cell 1 half end cell row cell 2 RS end cell equals cell 24 space cm end cell row RS equals cell fraction numerator 24 space cm over denominator 2 end fraction end cell row RS equals cell 12 space cm end cell end table

 

Kemudian perhatikan bahwa segitiga PRS dan segitiga QRS sebangun.

Dengan menggunakan kesebangunan pada segitiga, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell PS over RS end cell equals cell RS over SQ end cell row cell fraction numerator 12 square root of 3 space cm over denominator 12 space cm end fraction end cell equals cell fraction numerator 12 space cm over denominator SQ end fraction end cell row cell 12 square root of 3 space cm times SQ end cell equals cell 12 space cm cross times 12 space cm end cell row SQ equals cell fraction numerator down diagonal strike 12 space cm end strike cross times 12 space cm over denominator down diagonal strike 12 square root of 3 space down diagonal strike cm end fraction end cell row SQ equals cell fraction numerator 12 space cm over denominator square root of 3 end fraction end cell row SQ equals cell fraction numerator 12 space cm over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row SQ equals cell fraction numerator 12 square root of 3 space cm over denominator 3 end fraction end cell row SQ equals cell 4 square root of 3 space cm end cell end table

Sehingga diperoleh panjang sisi PQ, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row PQ equals cell PS plus SQ equals 12 square root of 3 space cm plus 4 square root of 3 space cm end cell row blank equals cell 16 square root of 3 space cm end cell end table

Maka, panjang sisi PQ adalah 16 square root of 3 space cm.

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