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Pada gambar segitiga PQRS, diketahui PS = 4 cm , QS = 9 cm , dan RS = 6 cm . b. Buktikan bahwa sudut PRQ siku-siku.

Pada gambar segitiga PQRS, diketahui , dan .

b. Buktikan bahwa sudut PRQ siku-siku.

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L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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Pembahasan

pertama, kita cari dulu panjang PR dan panajng QR. kemudian kita buktikan dengan teorema Pythagoras, terlihat bahwa ruas kiri sama dengan ruas kanan. Jadi, terbukti bahwa sudut PRQ siku-siku.

pertama, kita cari dulu panjang PR dan panajng QR.

PR equals square root of PS squared plus RS squared end root space space space space space space space space space space space space space space space space space space space space space QR equals square root of QS squared plus RS squared end root space space space space space equals square root of 4 squared plus 6 squared end root space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals square root of 9 squared plus 6 squared end root space space space space space equals square root of 16 plus 36 end root space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals square root of 81 plus 36 end root space space space space space equals square root of 52 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals square root of 117 space space space space space equals square root of 4 cross times 13 end root space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space square root of 9 cross times 13 end root space space space space space space equals 2 square root of 13 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 3 square root of 13 

kemudian kita buktikan dengan teorema Pythagoras,

P Q squared equals P R squared plus Q R squared space space space space rightwards arrow space space space 13 squared space... space open parentheses 2 square root of 13 close parentheses squared plus open parentheses 3 square root of 13 close parentheses squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 169 space... space 52 plus 117 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 169 equals 169

terlihat bahwa ruas kiri sama dengan ruas kanan.

Jadi, terbukti bahwa sudut PRQ siku-siku. 

 

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