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Diketahui kubus ABCD.EFGH memiliki panjang rusuk . Jarak antara titik C dengan bidang BDG adalah .... cm

Pertanyaan

Diketahui kubus ABCD.EFGH memiliki panjang rusuk begin mathsize 14px style 12 space cm end style. Jarak antara titik C dengan bidang BDG adalah .... cm

  1. begin mathsize 14px style 2 square root of 2 end style 

  2.  begin mathsize 14px style 2 square root of 3 end style 

  3. begin mathsize 14px style 3 square root of 2 end style  

  4. begin mathsize 14px style 3 square root of 3 end style 

  5. begin mathsize 14px style 4 square root of 3 end style  

Pembahasan Soal:

 

 

begin mathsize 14px style A C equals square root of A B squared plus B C to the power of 2 to the power of blank end exponent end root space space space space space equals square root of 12 squared plus 12 squared end root space space space space space equals square root of 12 squared cross times 2 end root space space space space space equals 12 square root of 2 C O equals 1 half cross times A C space space space space space equals 1 half cross times 12 square root of 2 space space space space space equals 6 square root of 2 end style 

begin mathsize 14px style G O equals square root of G C squared plus C O squared end root space space space space space equals square root of 12 squared plus open parentheses 6 square root of 2 close parentheses squared end root space space space space space equals square root of 144 plus 72 end root space space space space space equals square root of 216 space space space space space equals 6 square root of 6 end style 

lihat begin mathsize 14px style increment G C O end style

begin mathsize 14px style L u a s subscript G C O end subscript equals 1 half cross times G C cross times C O equals 1 half x G O cross times C P space space space space space space space space space space space space space space left right double arrow up diagonal strike 1 half end strike cross times 12 cross times up diagonal strike 6 square root of 2 equals up diagonal strike 1 half end strike cross times up diagonal strike 6 square root of 6 cross times C P space space space space space space space space space space space space space space left right double arrow C P equals fraction numerator 12 square root of 2 over denominator square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction space space space space space space space space space space space space space space left right double arrow C P equals fraction numerator 12 times 2 square root of 3 over denominator 6 end fraction space space space space space space space space space space space space space space space left right double arrow C P equals 4 square root of 3 space space space space space space space space space space space space space space space space space space space end style 

Jadi, jawaban yang tepat adalah E

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 08 Februari 2021

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