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Pertanyaan

Perhatikan gambar berikut Pada persegi panjang ABCD, diketahui u = D C dan v = BC Diketahui BP : PC = 1 : 3 dan DQ : QC = 1 : 2. Maka PQ ​ = ...

Perhatikan gambar berikut

Pada persegi panjang ABCD, diketahui dan Diketahui BP : PC = 1 : 3 dan DQ : QC = 1 : 2. Maka

  1. begin mathsize 14px style 2 over 3 v with rightwards arrow on top minus 3 over 4 u with rightwards arrow on top end style

  2. begin mathsize 14px style 1 fourth v with rightwards arrow on top minus 1 third u with rightwards arrow on top end style

  3. begin mathsize 14px style 3 over 4 v with rightwards arrow on top minus 2 over 3 u with rightwards arrow on top end style

  4. begin mathsize 14px style 1 fourth v with rightwards arrow on top plus 1 third u with rightwards arrow on top end style

  5. begin mathsize 14px style 3 over 4 v with rightwards arrow on top plus 2 over 3 u with rightwards arrow on top end style

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N. Indah

Master Teacher

Mahasiswa/Alumni Universitas Diponegoro

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa Karena BP : PC = 1 : 3, maka panjang . Karena searah dengan maka Kemudian karena DQ : QC = 1 : 2, maka panjang . Karena searah dengan maka Sehingga

Perhatikan bahwa

begin mathsize 14px style stack P Q with rightwards arrow on top equals stack P C with rightwards arrow on top plus stack C Q with rightwards arrow on top equals stack P C with rightwards arrow on top plus open parentheses negative stack Q C with rightwards arrow on top close parentheses equals stack P C with rightwards arrow on top minus stack Q C with rightwards arrow on top end style 

Karena BP : PC = 1 : 3, maka panjang begin mathsize 14px style P C equals 3 over 4 B C end style . Karena begin mathsize 14px style stack P C with rightwards arrow on top end style searah dengan begin mathsize 14px style stack B C with rightwards arrow on top end style maka begin mathsize 14px style stack P C with rightwards arrow on top equals 3 over 4 stack B C with rightwards arrow on top end style

Kemudian karena DQ : QC = 1 : 2, maka panjang begin mathsize 14px style Q C equals 2 over 3 D C end style . Karena begin mathsize 14px style stack Q C with rightwards arrow on top end style searah dengan begin mathsize 14px style stack D C with rightwards arrow on top end style maka begin mathsize 14px style stack Q C with rightwards arrow on top equals 2 over 3 stack D C with rightwards arrow on top end style

 

Sehingga

begin mathsize 14px style stack P Q with rightwards arrow on top equals stack P C with rightwards arrow on top minus stack Q C with rightwards arrow on top equals 3 over 4 stack B C with rightwards arrow on top minus 2 over 3 stack D C with rightwards arrow on top equals 3 over 4 v with rightwards arrow on top minus 2 over 3 u with rightwards arrow on top end style 

 

 

 

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