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Pada ΔABC, titik P dan Q masing-masing terletak pada sisi AB dan AC sehingga AP : PB = 2 : 3 dan AQ : QC = 1 : 4. Jika A B = p ​ dan BC = q ​ maka PQ ​ = ...

Pada ΔABC, titik P dan Q masing-masing terletak pada sisi AB dan AC sehingga AP : PB = 2 : 3 dan AQ : QC = 1 : 4. Jika dan maka ...

  1. begin mathsize 14px style 3 over 5 p with rightwards arrow on top plus 3 over 5 q with rightwards arrow on top end style

  2. begin mathsize 14px style negative 3 over 5 p with rightwards arrow on top plus 1 fifth q with rightwards arrow on top end style

  3. begin mathsize 14px style 3 over 5 p with rightwards arrow on top plus 1 fifth q with rightwards arrow on top end style

  4. begin mathsize 14px style negative 1 fifth p with rightwards arrow on top plus 1 fifth q with rightwards arrow on top end style

  5. begin mathsize 14px style 1 fifth p with rightwards arrow on top plus 1 fifth q with rightwards arrow on top end style

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Pembahasan

Perhatikan gambar dari ΔABC berikut ini Perhatikan bahwa Kemudian didapat bahwa Karena AP : PB = 2 : 3, maka Kemudian karena AQ : QC = 1 : 4, maka Sehingga

Perhatikan gambar dari ΔABC berikut ini

Perhatikan bahwa

begin mathsize 14px style stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top equals stack A C with rightwards arrow on top p with rightwards arrow on top plus q with rightwards arrow on top equals stack A C with rightwards arrow on top end style 

Kemudian didapat bahwa

begin mathsize 14px style stack P Q with rightwards arrow on top equals stack P A with rightwards arrow on top plus stack A Q with rightwards arrow on top end style 

 

Karena AP : PB = 2 : 3, maka begin mathsize 14px style stack P A with rightwards arrow on top equals 2 over 5 stack B A with rightwards arrow on top end style

Kemudian karena AQ : QC = 1 : 4, maka begin mathsize 14px style stack A Q with rightwards arrow on top equals 1 fifth stack A C with rightwards arrow on top end style

Sehingga

begin mathsize 14px style stack P Q with rightwards arrow on top equals stack P A with rightwards arrow on top plus stack A Q with rightwards arrow on top equals 2 over 5 stack B A with rightwards arrow on top plus 1 fifth stack A C with rightwards arrow on top equals 2 over 5 open parentheses negative stack A B with rightwards arrow on top close parentheses plus 1 fifth stack A C with rightwards arrow on top equals negative 2 over 5 stack A B with rightwards arrow on top plus 1 fifth stack A C with rightwards arrow on top equals negative 2 over 5 p with rightwards arrow on top plus 1 fifth open parentheses p with rightwards arrow on top plus q with rightwards arrow on top close parentheses equals negative 2 over 5 p with rightwards arrow on top plus 1 fifth p with rightwards arrow on top plus 1 fifth q with rightwards arrow on top equals negative 1 fifth p with rightwards arrow on top plus 1 fifth q with rightwards arrow on top end style 

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