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Perhatikan gambar di samping! Jika trapesium  dan  sebangun, maka tentukan panjang , , dan .

Pertanyaan

Perhatikan gambar di samping! Jika trapesium begin mathsize 14px style ABCD end style dan size 14px PQRS sebangun, maka tentukan panjang begin mathsize 14px style QR end stylebegin mathsize 14px style P S end style, dan size 14px DC.

  1. begin mathsize 14px style horizontal ellipsis end style 

  2. begin mathsize 14px style horizontal ellipsis end style 

Pembahasan Soal:

Karena trapesium begin mathsize 14px style ABCD end style dan size 14px PQRS sebangun, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB over PQ end cell equals cell BC over QR end cell row cell fraction numerator 6 space cm over denominator 9 space cm end fraction end cell equals cell fraction numerator 5 space cm over denominator QR end fraction end cell row cell 2 over 3 end cell equals cell fraction numerator 5 space cm over denominator QR end fraction end cell row cell 2 QR end cell equals cell 15 space cm end cell row QR equals cell 15 over 2 cm end cell end table end style

Selanjutnya,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB over PQ end cell equals cell DC over SR end cell row cell fraction numerator 6 space cm over denominator 9 space cm end fraction end cell equals cell fraction numerator DC over denominator 6 space cm end fraction end cell row cell 2 over 3 end cell equals cell fraction numerator DC over denominator 6 space cm end fraction end cell row cell 3 DC end cell equals cell 12 space cm end cell row DC equals cell 4 space cm end cell end table end style

Terakhir, perhatikan gambar berikut:

Karena begin mathsize 14px style SR end style dan size 14px PQ sejajar, maka kita buat garis begin mathsize 14px style RT end style sejajar begin mathsize 14px style PS end style sehingga panjang begin mathsize 14px style SR equals PT equals 6 space cm end style, panjang begin mathsize 14px style TQ equals PQ minus PT equals 3 space cm end style, dan panjang begin mathsize 14px style PS equals TR end style. Karena begin mathsize 14px style increment RTQ end style siku-siku, maka kita gunakan Teorema Pythagoras untuk menentukan panjang begin mathsize 14px style TR end style. Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell TR squared end cell equals cell QR squared minus TQ squared end cell row cell TR squared end cell equals cell open parentheses 15 over 2 space cm close parentheses squared minus open parentheses 3 space cm close parentheses squared end cell row cell TR squared end cell equals cell 225 over 4 space cm squared minus 9 space cm squared end cell row cell TR squared end cell equals cell fraction numerator 225 minus 36 over denominator 4 end fraction space cm squared end cell row cell TR squared end cell equals cell 189 over 4 space cm squared end cell row TR equals cell plus-or-minus square root of 189 over 4 space cm squared end root end cell row TR equals cell plus-or-minus square root of fraction numerator 9 cross times 21 over denominator 4 end fraction space cm squared end root end cell row TR equals cell plus-or-minus 3 over 2 square root of 21 space cm end cell end table end style

Karena panjang sisi segitiga selalu positif, maka panjang begin mathsize 14px style PS equals TR equals 3 over 2 square root of 21 space cm end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 10 Februari 2021

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