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Pertanyaan

Perhatikan gambar berikut. Jika AB = 15 cm, BC = 8 cm, dan AC = 13 cm, maka panjang jari-jari lingkaran dalam segitiga ABC tersebut adalah ….

Perhatikan gambar berikut.

Jika AB = 15 cm, BC = 8 cm, dan AC = 13 cm, maka panjang jari-jari lingkaran dalam segitiga ABC tersebut adalah ….

  1. begin mathsize 14px style fraction numerator 5 square root of 3 over denominator 3 end fraction space cm end style  

  2. begin mathsize 14px style fraction numerator 20 square root of 3 over denominator 3 end fraction space cm end style   

  3. begin mathsize 14px style fraction numerator 5 square root of 6 over denominator 18 end fraction space cm end style  

  4. begin mathsize 14px style fraction numerator 10 square root of 6 over denominator 9 end fraction space cm end style  

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R. Bella

Master Teacher

Mahasiswa/Alumni UIN Syarif Hidayatullah Jakarta

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Pembahasan

Diketahui AB = a = 15 cm, BC = b = 8 cm, dan AC = c = 13 cm, maka Sehingga

Diketahui AB = a = 15 cm, BC = b = 8 cm, dan AC = c = 13 cm, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight s equals cell 1 half left parenthesis straight a plus straight b plus straight c right parenthesis end cell row blank equals cell 1 half left parenthesis 15 plus 8 plus 13 right parenthesis end cell row blank equals cell 1 half left parenthesis 36 right parenthesis end cell row blank equals 18 end table end style   

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight r equals cell fraction numerator square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root over denominator straight s end fraction end cell row blank equals cell square root of fraction numerator 18 left parenthesis 18 minus 15 right parenthesis left parenthesis 18 minus 8 right parenthesis left parenthesis 18 minus 13 right parenthesis over denominator 18 end fraction end root end cell row blank equals cell square root of fraction numerator 18 times 3 times 10 times 5 over denominator 18 end fraction end root end cell row blank equals cell fraction numerator square root of 9 times 2 times 3 times 2 times 5 times 5 end root over denominator 18 end fraction end cell row blank equals cell fraction numerator square root of 9 times 2 squared times 5 squared times 3 end root over denominator 18 end fraction end cell row blank equals cell fraction numerator 3 times 2 times 5 square root of 3 over denominator 18 cubed end fraction end cell row blank equals cell fraction numerator horizontal strike 3 times 2 end strike times 5 square root of 3 over denominator 18 cubed end fraction end cell row blank equals cell fraction numerator 5 square root of 3 over denominator 3 end fraction end cell end table end style   

 

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