Pada limas T.PQR di atas, PQ⊥RQ, PR⊥TR, dan TR⊥QR. Panjang PQ=15 cm, PR=17 cm, dan TR=40​ cm. a. Hitunglah panjang QR, PT, dan QT b. Buktikan bahwa △PQT siku-siku di Q!

Pertanyaan


Pada limas T.PQR di atas, PQ perpendicular RQPR perpendicular TR, dan TR perpendicular QR. Panjang PQ equals 15 space cmPR equals 17 space cm, dan TR equals square root of 40 space cm.

a. Hitunglah panjang QR, PT, dan QT

b. Buktikan bahwa increment PQT siku-siku di Q!

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

a. Dengan menggunakan teorema Pythagoras maka diperoleh panjang QR, PT, dan QT:

table attributes columnalign right center left columnspacing 0px end attributes row QR equals cell square root of PR squared minus PQ squared end root end cell row blank equals cell square root of 17 squared minus 15 squared end root end cell row blank equals cell square root of 289 minus 225 end root end cell row blank equals cell square root of 64 end cell row blank equals cell 8 space cm end cell row PT equals cell square root of PR squared plus RT squared end root end cell row blank equals cell square root of 17 squared plus open parentheses square root of 40 close parentheses squared end root end cell row blank equals cell square root of 289 plus 40 end root end cell row blank equals cell square root of 329 space cm end cell row QT equals cell square root of TR squared minus QR squared end root end cell row blank equals cell square root of open parentheses square root of 40 close parentheses squared plus 8 squared end root end cell row blank equals cell square root of 40 plus 64 end root end cell row blank equals cell square root of 104 end cell row blank equals cell 2 square root of 26 space cm end cell end table 

Dengan demikian diperoleh panjang QR equals 8 space cmPT equals square root of 329 space cm, dan QT equals 2 square root of 26 space cm.

b.  increment PQT terbukti siku-siku di Q apabila memenuhi teorema Pythagoras dimana PT adalah sisi miring maka:

table attributes columnalign right center left columnspacing 0px end attributes row PT equals cell square root of PQ squared plus QT squared end root end cell row cell square root of 329 end cell equals cell square root of 15 squared plus open parentheses 2 square root of 26 close parentheses squared end root end cell row cell square root of 329 end cell equals cell square root of 225 plus open parentheses 4 cross times 26 close parentheses end root end cell row cell square root of 329 end cell equals cell square root of 225 plus 104 end root end cell row cell square root of 329 end cell equals cell square root of 329 end cell end table 

Dengan demikian terbukti bahwa increment PQT siku-siku di Q.

 

67

0.0 (0 rating)

Pertanyaan serupa

1. Perhatikan gambar di samping. Panjang x adalah...cm.

3rb+

4.7

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Fitur Roboguru

Topik Roboguru

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia