Kubus ABCD.EFGH panjang sisi 10 cm. Titik P merupakan perpotongan diagonal bidang ABCD. Tentukan jarak titik P ke G!

Pertanyaan

Kubus ABCD.EFGH panjang sisi 10 cm. Titik P merupakan perpotongan diagonal bidang ABCD. Tentukan jarak titik P ke G!

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jarak titik P ke G adalah 5 square root of 6 cm.

Pembahasan

Dari soal dapat digambarkan menjadi:

Jarak titik P ke titik G dapat kita cari menggunakan Teorema Pythagoras. Tetapi kita harus mencari panjang PC. Karena PC adalah setengah dari diagonal sisi AC, maka kita akan mencari AC

 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank AC end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of AB squared plus BC squared end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 10 squared plus 10 squared end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table space space space space space table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 100 plus 100 end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table space space space space space table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 200 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table space space space space space table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 times 100 end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table space space space space space table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cm end table

 

Maka:

PC equals 1 half AC equals 1 half cross times 10 square root of 2 equals 5 square root of 2 space cm space 

Jarak titik P ke G adalah PG. Sehingga:

PG equals square root of PC squared plus CG squared end root PG equals square root of open parentheses 5 square root of 2 close parentheses squared plus 10 squared end root PG equals square root of 25 times 2 plus 100 end root PG equals square root of 50 plus 100 end root PG equals square root of 150 PG equals square root of 25 times 6 end root PG equals 5 square root of 6 

Jadi, jarak titik P ke G adalah 5 square root of 6 cm.

1rb+

4.0 (1 rating)

Pertanyaan serupa

Diketahui kubus ABCD.EFGH dengan AB=8 cm. Titik P terletak ditengah-tengah garis FG. Jarak titik A ke titik P adalah .... cm

180

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