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Pada  diketahui , , dan . b. Buktikan  siku-siku di titik .

Pertanyaan

Pada begin mathsize 14px style triangle P Q R end style diketahui begin mathsize 14px style P S equals 2 cm end stylebegin mathsize 14px style Q S equals 8 cm end style, dan begin mathsize 14px style R S equals 4 cm end style.

b. Buktikan begin mathsize 14px style triangle P Q R end style siku-siku di titik begin mathsize 14px style R end style.

Pembahasan Soal:

Pada begin mathsize 14px style triangle P Q R end style diketahui begin mathsize 14px style P S equals 2 cm end stylebegin mathsize 14px style Q S equals 8 cm end style, dan begin mathsize 14px style R S equals 4 cm end style.

b. Akan dicari panjang begin mathsize 14px style P R end style dan begin mathsize 14px style Q R end style terlebih dahulu menggunakan Teorema Pythagoras.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P R end cell equals cell square root of P S squared plus R S squared end root end cell row blank equals cell square root of 2 squared plus 4 squared end root end cell row blank equals cell square root of 4 plus 16 end root end cell row blank equals cell square root of 20 end cell row blank equals cell 2 square root of 5 end cell end table end style 
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Q R end cell equals cell square root of Q S squared plus R S squared end root end cell row blank equals cell square root of 8 squared plus 4 squared end root end cell row blank equals cell square root of 64 plus 16 end root end cell row blank equals cell square root of 80 end cell row blank equals cell 4 square root of 5 end cell end table end style 


Jadi, diperoleh begin mathsize 14px style P R equals 2 square root of 5 cm end style dan begin mathsize 14px style Q R equals 4 square root of 5 cm end style.
 

Selanjutnya akan ditunjukkan apakah begin mathsize 14px style P Q squared equals P R squared plus Q R squared end style. JIka benar, berarti begin mathsize 14px style triangle P Q R end style siku-siku di begin mathsize 14px style R end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P R squared plus Q R squared end cell equals cell open parentheses 2 square root of 5 close parentheses squared plus open parentheses 4 square root of 5 close parentheses squared end cell row blank equals cell 20 plus 80 end cell row blank equals 100 row blank equals cell 10 squared end cell row blank equals cell P Q squared end cell end table end style 
 

Terbukti begin mathsize 14px style P Q squared equals P R squared plus Q R squared end style, berarti begin mathsize 14px style triangle P Q R end style siku-siku di begin mathsize 14px style R end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 21 Mei 2021

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