Pertanyaan

Diketahui kubus ABCD.EFGH dengan titik P pada AG sehingga AP : PG = 3 : 1. Jika panjang rusuk 12, maka jarak P ke bidang BDG adalah…

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Habis dalam

Klaim

M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

Perhatikan persegi panjang ACGE Luas ΔGQR = Luas Δ ACG – (Luas Δ GQC + Luas Δ AQP )

Perhatikan persegi panjang ACGE

Luas ΔGQR = Luas ΔACG – (Luas ΔGQC + Luas ΔAQP)

$fraction numerator G Q cross times x over denominator 2 end fraction equals fraction numerator A C cross times C G over denominator 2 end fraction minus open parentheses fraction numerator Q C cross times C G over denominator 2 end fraction plus fraction numerator A Q cross times P R over denominator 2 end fraction close parentheses fraction numerator 6 square root of 6 space cross times space x over denominator 2 end fraction equals fraction numerator 12 square root of 2 space cross times space 12 over denominator 2 end fraction minus open parentheses fraction numerator 6 square root of 2 space cross times space 12 over denominator 2 end fraction plus fraction numerator 6 square root of 2 space cross times space begin display style 3 over 4 end style space cross times space 12 over denominator 2 end fraction close parentheses 6 square root of 6 cross times x equals 144 square root of 2 minus left parenthesis 72 square root of 2 plus 54 square root of 2 right parenthesis 6 square root of 6 cross times x equals 18 square root of 2 x equals fraction numerator 18 square root of 2 over denominator 6 square root of 6 end fraction x equals fraction numerator 3 over denominator square root of 3 end fraction x equals 3 over 3 square root of 3 equals square root of 3$