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Soal Tantangan Pada gambar berikut ini, diketahui...

Soal Tantangan

Pada gambar berikut ini, diketahui AB = BC = 10 cm dan garis AD adalah garis bagi. Panjang, tentukan panjang BD!space

  1. begin mathsize 14px style... end style

  2. undefined

Jawaban:

Perhatikan gambar berikut :

Diketahui : 
AB= 10 cm
BC= 10 cm
begin mathsize 14px style angle B A D equals angle B A C end style 

Ditanya :
Panjang BD = ?

Jawab :

Pertama, cari panjang AC gunakan rumus phytagoras :

begin mathsize 14px style A C equals square root of A B squared plus B C squared end root A C equals square root of 10 squared plus 10 squared end root A C equals square root of 200 A C equals square root of 100 cross times 2 end root A C equals 10 square root of 2 end style 

Perhatikan gambar berikut :

 

Berdasarkan teorema garis bagi, maka segitiga ABD kongruen dengan segitiga ADE, sehingga BD=ED, Kemudian :

begin mathsize 14px style L. increment A B C equals L. increment A B D plus L. increment A D C 1 half cross times A B cross times B C equals 1 half A B cross times B D plus 1 half cross times A C cross times D E up diagonal strike 1 half end strike cross times 10 cross times 10 equals up diagonal strike 1 half end strike 10 cross times B D plus up diagonal strike 1 half end strike cross times 10 square root of 2 cross times B D 100 equals 10 space B D plus 10 square root of 2 B D 100 equals left parenthesis 10 plus 10 square root of 2 right parenthesis B D B D equals fraction numerator 100 over denominator open parentheses 10 plus 10 square root of 2 close parentheses end fraction B D equals fraction numerator 10 over denominator open parentheses 1 plus square root of 2 close parentheses end fraction B D equals fraction numerator 10 over denominator open parentheses 1 plus square root of 2 close parentheses end fraction cross times fraction numerator open parentheses 1 minus square root of 2 close parentheses over denominator 1 minus square root of 2 end fraction B D equals fraction numerator 10 open parentheses 1 minus square root of 2 close parentheses over denominator open parentheses 1 minus 2 close parentheses end fraction B D equals fraction numerator 10 open parentheses 1 minus square root of 2 close parentheses over denominator open parentheses negative 1 close parentheses end fraction B D equals negative 10 left parenthesis 1 minus square root of 2 right parenthesis B D equals negative 10 plus 10 square root of 2 space B D equals 4 comma 14 space c m  end style 

Jadi, panjang BD adalah begin mathsize 14px style 4 comma 14 space c m end style 

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