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Kubus PQRS.TUVW mempunyai panjang rusuk . Titik O ...

Kubus PQRS.TUVW mempunyai panjang rusuk begin mathsize 14px style 10 space cm end style. Titik O pada PQ sehingga begin mathsize 14px style PO space colon space OQ equals 2 space colon space 3 end style dan X pada RV sehingga begin mathsize 14px style RV equals 4 RX end style. Tentukan:

e. Jarak titik T ke X,

Jawaban:

Perhatikan gambar berikut!

Perhatikan segitiga siku-siku TVX.

table attributes columnalign right center left columnspacing 0px end attributes row cell RV space end cell equals cell space 4 RX end cell row 10 equals cell 4 RX end cell row RX equals cell 10 over 4 end cell row blank equals cell 5 over 2 end cell row VX equals cell RV minus RX end cell row blank equals cell 10 minus 5 over 2 end cell row blank equals cell 20 over 2 minus 5 over 2 end cell row blank equals cell 15 over 2 end cell row TV equals cell s square root of 2 space left parenthesis diagonal space sisi space kubus right parenthesis end cell row blank equals cell 10 square root of 2 space cm end cell row TX equals cell square root of TV squared plus VX squared end root end cell row blank equals cell square root of open parentheses 10 square root of 2 close parentheses squared plus open parentheses 15 over 2 close parentheses squared end root end cell row blank equals cell square root of 200 plus 225 over 4 end root end cell row blank equals cell square root of fraction numerator 800 plus 225 over denominator 2 end fraction end root end cell row blank equals cell square root of 1025 over 4 end root end cell row blank equals cell square root of 1 fourth times 1025 end root end cell row blank equals cell 1 half square root of 1025 space cm end cell end table 

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