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Perhatikan gambar berikut!   Panjang AE adalahh ...

Pertanyaan

Perhatikan gambar berikut!

 

Panjang AE adalahh ... 

  1. 6 comma 60 space text cm end text 

  2. 7 comma 15 space text cm end text 

  3. 9 comma 60 space text cm end text 

  4. 10 comma 40 space text cm end text 

Pembahasan Soal:

Lihat segitiga ADC, berdasarkan teorema phytagoras diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell A C end cell equals cell square root of A D squared plus D C squared end root end cell row blank equals cell square root of 5 squared plus 12 squared end root end cell row blank equals cell square root of 25 plus 144 end root end cell row blank equals cell square root of 169 end cell row blank equals 13 end table 

Lihat segitiga ADC, berdasarkan teorema phytagoras diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell A C end cell equals cell square root of D B squared plus D C squared end root end cell row blank equals cell square root of 16 squared plus 12 squared end root end cell row blank equals cell square root of 256 plus 144 end root end cell row blank equals cell square root of 400 end cell row blank equals 20 end table 

Selanjutnya, perhatikan segitiga AEC dan AEB mempunyai sisi yang sama yaitu AE. Dimisalkan panjang EB adalah x, maka panjang EC adalah (20-x), sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis A E subscript triangle A E C end subscript right parenthesis squared end cell equals cell left parenthesis A E subscript triangle A E B end subscript right parenthesis squared space end cell row cell A C squared minus E C squared end cell equals cell A B squared minus E B squared end cell row cell 13 squared minus left parenthesis 20 minus x right parenthesis squared end cell equals cell 11 squared minus x squared end cell row cell 169 minus left parenthesis 400 minus 40 x plus x squared right parenthesis end cell equals cell 121 minus x squared end cell row cell negative x squared plus x squared plus 40 x end cell equals cell 121 minus 169 plus 400 end cell row cell 40 x end cell equals 352 row x equals cell 8 comma 8 end cell end table 

Maka, panjang AE dapat dicari sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell A E end cell equals cell square root of A B squared minus E B squared end root end cell row blank equals cell square root of 11 squared minus 8 comma 8 squared end root end cell row blank equals cell square root of 121 minus 77 comma 44 end root end cell row blank equals cell square root of 43 comma 56 end root end cell row blank equals cell 6 comma 6 end cell end table 

Oleh karena itu, jawaban yang benar adalah A.  

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 06 Mei 2021

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