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Diketahui sebuah balok ABCD.EFGH dengan  , , dan ....

Diketahui sebuah balok ABCD.EFGH dengan begin mathsize 14px style AB equals 4 space cm end style , begin mathsize 14px style B C equals 3 space cm end style, dan begin mathsize 14px style CG equals 5 space cm end style. Tentukan jarak titik F ke garis:

c. DG

Jawaban:

Diketahui:

Bangun ruang balok.

Panjang sisi begin mathsize 14px style AB equals 4 space cm end stylebegin mathsize 14px style B C equals 3 space cm end style, dan begin mathsize 14px style CG equals 5 space cm end style.

Digambarkan sebagai berikut:

Jarak antara titik dengan garis harus memiliki syarat titik tegak lurus dengan garis tersebut.

 

c. DG

Digambarkan sebagai berikut:

Tentukan terlebih dahulu panjang DG dari segitiga CDG, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell DG squared end cell equals cell CD squared plus CG squared end cell row DG equals cell square root of CD squared plus CG squared end root end cell row DG equals cell square root of 4 squared plus 5 squared end root end cell row DG equals cell square root of 16 plus 25 end root end cell row DG equals cell square root of 41 end cell row DG equals cell 6 comma 40312 end cell row DG almost equal to cell 6 space cm end cell end table end style

Tentukan panjang BD dari segitiga ABD, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell BD squared end cell equals cell AB squared plus AD squared end cell row BD equals cell square root of AB squared plus AD squared end root end cell row BD equals cell square root of 4 squared plus 3 squared end root end cell row BD equals cell square root of 16 plus 9 end root end cell row BD equals cell square root of 25 end cell row BD equals cell 5 space cm end cell end table end style

Kemudian tentukan panjang DF dari segitiga BDF, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell DF squared end cell equals cell BD squared plus BF squared end cell row DF equals cell square root of BD squared plus BF squared end root end cell row DF equals cell square root of 5 squared plus 5 squared end root end cell row DF equals cell square root of 25 plus 25 end root end cell row DF equals cell square root of 50 end cell row DF equals cell square root of 25 cross times 2 end root end cell row DF equals cell 5 square root of 2 end cell row DF equals cell 7 comma 07107 end cell row DF almost equal to cell 7 space cm end cell end table end style

Sehingga digambarkan sebagai berikut:

Karena segitiga DFG merupakan segitiga sembarang, maka hitung luas segitiga menggunakan rumus heron.

Setengah keliling dari segitiga DFG, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight s equals cell fraction numerator CF plus FG plus DG over denominator 2 end fraction end cell row blank equals cell fraction numerator 7 plus 3 plus 6 over denominator 2 end fraction end cell row blank equals cell 16 over 2 end cell row blank equals cell 8 space cm end cell end table end style

Sehingga,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight L equals cell square root of straight s open parentheses straight s minus DF close parentheses open parentheses straight s minus FG close parentheses open parentheses straight s minus DG close parentheses end root end cell row blank equals cell square root of 8 open parentheses 8 minus 7 close parentheses open parentheses 8 minus 3 close parentheses open parentheses 8 minus 6 close parentheses end root end cell row blank equals cell square root of 8 open parentheses 1 close parentheses open parentheses 5 close parentheses open parentheses 2 close parentheses end root end cell row blank equals cell square root of 80 end cell row blank equals cell square root of 16 cross times 5 end root end cell row blank equals cell 4 square root of 5 end cell row blank equals cell 8 comma 94427 end cell row blank almost equal to cell 9 space cm squared end cell end table end style

Tinggi segitiga DFG, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight L equals cell 1 half cross times DG cross times FO end cell row 9 equals cell 1 half cross times 6 cross times FO end cell row 9 equals cell 3 FO end cell row cell 3 FO end cell equals 9 row FO equals cell 9 over 3 end cell row FO equals cell 3 space cm end cell end table end style

Maka, jarak titik F ke garis DG adalah begin mathsize 14px style 3 space cm end style.

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