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 $\style{font-size:14px}{\triangle\mathrm{NLM}}$ adalah segitiga siku-siku dengan PQ sejajar dengan LM.

Jika luas $\style{font-size:14px}{\triangle\mathrm{PNQ}=8\;\mathrm{cm}^2}$ dan $\style{font-size:14px}{\triangle\mathrm{LPQ}=16\;\mathrm{cm}^2}$ , maka luas $\style{font-size:14px}{\triangle\mathrm{LQM}}$ adalah $\style{font-size:14px}\dots$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui luas , 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 ,

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

Karena 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 dan . Karena , maka (sudut sehadap). Selanjutnya, karena keduanya adalah segitiga siku-siku, serta memiliki sudut bersama di ,maka dan 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 adalah