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Perhatikan gambar di bawah ini! Tentukan panjan...

Perhatikan gambar di bawah ini!

Tentukan panjang EF, jika titik E dan titik F berturut-turut adalah titik tengah diagonal DB dan diagonal CA!

Jawaban:

Misalkan titik potong diagonal DB dan diagonal CA adalah begin mathsize 14px style straight O end style maka:

begin mathsize 14px style increment AOB comma space increment EOF space dan space increment DOC end style adalah 3 segitiga sama kaki yang sebangun.

dari begin mathsize 14px style increment AOB space dan space increment DOC end style diperoleh perbandingan sisi yang sama besar, yaitu: 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell DO over OB end cell equals cell DC over AB end cell row cell DO over OB end cell equals cell fraction numerator 24 space cm over denominator 12 space cm end fraction end cell row cell DO over OB end cell equals 2 row DO equals cell 2 times OB end cell end table end style 

titik E adalah titik tengah DB sehingga begin mathsize 14px style DB equals 2 times BE end style maka:

table attributes columnalign right center left columnspacing 0px end attributes row size 14px DB size 14px equals cell size 14px DO size 14px plus size 14px OB end cell row cell size 14px 2 size 14px times size 14px BE end cell size 14px equals cell size 14px DO size 14px plus size 14px OB end cell row cell size 14px 2 size 14px times size 14px BE end cell size 14px equals cell size 14px 2 size 14px times size 14px OB size 14px plus size 14px OB end cell row cell size 14px 2 size 14px times size 14px BE end cell size 14px equals cell size 14px 3 size 14px times size 14px OB end cell row size 14px BE size 14px equals cell size 14px 3 over size 14px 2 size 14px times size 14px OB end cell row size 14px BE size 14px equals cell size 14px 3 over size 14px 2 size 14px times size 14px OB end cell row cell size 14px EO size 14px plus size 14px OB end cell size 14px equals cell size 14px 3 over size 14px 2 size 14px times size 14px OB end cell row size 14px EO size 14px equals cell size 14px 3 over size 14px 2 size 14px times size 14px OB size 14px minus size 14px OB end cell row blank size 14px equals cell size 14px 1 over size 14px 2 size 14px times size 14px OB end cell end table 

Dari begin mathsize 14px style increment AOB space dan space increment EOF end style yang sebangun maka diperoleh perbandingan yang sama besar, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell EO over OB end cell equals cell EF over AB end cell row cell fraction numerator begin display style 1 half end style times OB over denominator OB end fraction end cell equals cell fraction numerator EF over denominator 12 space cm end fraction end cell row cell fraction numerator begin display style 1 end style over denominator 2 end fraction end cell equals cell fraction numerator EF over denominator 12 space cm end fraction end cell row cell fraction numerator begin display style 12 space cm end style over denominator 2 end fraction end cell equals EF row cell 6 space cm end cell equals EF end table end style 

Jadi, Panjang begin mathsize 14px style EF equals 6 space cm end style.

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