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Diketahui △NLM adalah segitiga siku-siku dengan PQ sejajar dengan LM. Jika luas △PNQ=8 cm2 dan △LPQ=16 cm2, maka luas △LQM adalah …

Pertanyaan

Diketahui begin mathsize 14px style increment NLM end style adalah segitiga siku-siku dengan PQ sejajar dengan LM.

Jika luas begin mathsize 14px style increment PNQ equals 8 space cm squared end style dan begin mathsize 14px style increment LPQ equals 16 space cm squared end style, maka luas begin mathsize 14px style increment LQM end style adalah undefined

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A. Acfreelance

Master Teacher

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Pembahasan

Diketahui luas begin mathsize 14px style increment PNQ equals 8 space cm squared end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator NP cross times PQ over denominator 2 end fraction end cell equals cell 8 space cm squared end cell row cell NP cross times PQ end cell equals cell 16 space cm squared end cell row PQ equals cell fraction numerator 16 space cm squared over denominator NP end fraction end cell end table end style

Selanjutnya diketahui begin mathsize 14px style increment LPQ equals 16 space cm squared end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator LP cross times PQ over denominator 2 end fraction end cell equals cell 16 space cm squared end cell row cell straight L straight P cross times PQ end cell equals cell 32 space cm squared end cell row PQ equals cell fraction numerator 32 space cm squared over denominator LP end fraction end cell end table end style

Karena begin mathsize 14px style PQ equals PQ end style maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell up diagonal strike 16 space cm squared end strike to the power of 1 over NP end cell equals cell up diagonal strike 32 space cm squared end strike squared over LP end cell row LP equals cell 2 NP end cell end table end style

sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row NL equals cell NP plus LP end cell row blank equals cell NP plus 2 NP end cell row blank equals cell 3 NP end cell end table end style

Berikutnya, perhatikan begin mathsize 14px style increment NPQ end style dan begin mathsize 14px style increment NLM end style. Karena begin mathsize 14px style PQ divided by divided by LM end style, maka begin mathsize 14px style angle NQP equals angle NML end style (sudut sehadap). Selanjutnya, karena keduanya adalah segitiga siku-siku, serta memiliki sudut bersama di begin mathsize 14px style straight N end style,maka begin mathsize 14px style increment NPQ end style dan begin mathsize 14px style increment NLM end style sebangun. Akibatnya

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell NP over NL end cell equals cell PQ over LM end cell row cell fraction numerator NP over denominator 3 NP end fraction end cell equals cell fraction numerator begin display style fraction numerator 16 space cm squared over denominator NP end fraction end style over denominator LM end fraction end cell row cell fraction numerator up diagonal strike NP over denominator 3 up diagonal strike NP end fraction end cell equals cell fraction numerator 16 space cm squared over denominator NP cross times LM end fraction end cell row cell NP cross times LM end cell equals cell 48 space cm squared end cell end table end style

Lalu perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript increment NLM end subscript end cell equals cell fraction numerator NL cross times LM over denominator 2 end fraction end cell row blank equals cell fraction numerator 3 NP cross times LM over denominator 2 end fraction end cell row blank equals cell fraction numerator 3 cross times 48 space cm squared over denominator 2 end fraction end cell row blank equals cell 72 space cm squared end cell end table end style

Dengan demikian, luas begin mathsize 14px style increment LQM end style adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript increment LQM end subscript end cell equals cell straight L subscript increment NLM end subscript minus straight L subscript increment PQN end subscript minus straight L subscript increment LPQ end subscript end cell row blank equals cell 72 space cm squared minus 8 space cm squared minus 16 space cm squared end cell row blank equals cell 48 space cm squared end cell end table end style

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