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Math Help - Similarity.....

  1. #1
    Member
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    jharkhand
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    Arrow Similarity.....

    In traingle ABC, PQ//BC, PR//BQ and 2AP=3PB, calculate:
    1. triangle ARP:triangle AQP,
    2. triangle AQP:triangle ABC,
    3. triangle ARP:triangle ABC,
    4. triangle AQP:trapezium PQCB.

    Would somebody plz be kind enough to post the solution??
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  2. #2
    MHF Contributor red_dog's Avatar
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    1) \frac{AP}{PB}=\frac{AR}{RQ}=\frac{3}{2}\Rightarrow \frac{AR}{AQ}=\frac{3}{5}\Rightarrow\frac{h_{ARP}}  {h_{AQP}}=\frac{3}{5}

    Then, \frac{S_{ARP}}{S_{AQP}}=\frac{3}{5}

    2) \frac{AP}{AB}=\frac{3}{5}\Rightarrow\frac{S_{AQP}}  {S_{ABC}}=\frac{9}{25}

    3) S_{ARP}=\frac{3}{5}S_{AQP}=\frac{3}{5}\cdot\frac{9  }{25}S_{ABC}=\frac{27}{125}S_{ABC}\Rightarrow\frac  {S_{ARP}}{S_{ABC}}=\frac{27}{125}

    4) S_{PQCB}=S_{ABC}-S_{APQ}=\frac{25}{9}S_{APQ}-S_{APQ}=\frac{16}{9}S_{APQ}\Rightarrow\frac{S_{PQC  B}}{S_{APQ}}=\frac{16}{9}
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