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 ….

$begin mathsize 14px style fraction numerator 5 square root of 3 over denominator 3 end fraction space cm end style$
$begin mathsize 14px style fraction numerator 20 square root of 3 over denominator 3 end fraction space cm end style$
$begin mathsize 14px style fraction numerator 5 square root of 6 over denominator 18 end fraction space cm end style$
$begin mathsize 14px style fraction numerator 10 square root of 6 over denominator 9 end fraction space cm end style$

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Jawaban terverifikasi

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

Sehingga

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