Pertanyaan

Diketahui O(0, 0), A(1, 0), B(2, 0), C(2, y), dan D(0, y). Nilai y → 1 lim keliling ACD keliling ABCD adalah ….

Diketahui O(0, 0), A(1, 0), B(2, 0), C(2, y), dan D(0, y). Nilai $y \to 1 lim \frac{keliling ABCD}{keliling ACD}$ adalah ….

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S. Suharni

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Berdasarkan informasi pada gambar, kita peroleh gambar berikut! Perhatikan segitiga ACD berikut! Didapat AC = AD = AC = AD = Kemudian, kita dapat menghitung sebagai berikut. Jadi, jawaban yang tepat adalah D.

Berdasarkan informasi pada gambar, kita peroleh gambar berikut!

Perhatikan segitiga ACD berikut!

Didapat

AC = AD =

Kemudian, kita dapat menghitung $begin mathsize 14px style limit as y rightwards arrow 1 of invisible function application fraction numerator keliling blank ABCD over denominator keliling blank ACD end fraction end style$ sebagai berikut.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as y rightwards arrow 1 of invisible function application fraction numerator k e l i l i n g blank A B C D blank over denominator k e l i l i n g blank A C D end fraction end cell equals cell limit as y rightwards arrow 1 of invisible function application fraction numerator A B plus B C plus C D plus A D over denominator A C plus C D plus A D end fraction end cell row blank equals cell limit as y rightwards arrow 1 of invisible function application fraction numerator 1 plus y plus 2 plus square root of 1 plus y squared end root over denominator square root of 1 plus y squared end root plus 2 plus square root of 1 plus y squared end root end fraction end cell row blank equals cell fraction numerator 1 plus 1 plus 2 plus square root of 1 plus 1 squared end root over denominator square root of 1 plus 1 squared end root plus square root of 1 plus 1 squared end root plus 2 end fraction end cell row blank equals cell fraction numerator 4 plus square root of 2 over denominator square root of 2 plus square root of 2 plus 2 end fraction end cell row blank equals cell fraction numerator 4 plus square root of 2 over denominator 2 square root of 2 plus 2 end fraction end cell row blank equals cell fraction numerator 4 plus square root of 2 over denominator 2 square root of 2 plus 2 end fraction times fraction numerator 2 square root of 2 minus 2 over denominator 2 square root of 2 minus 2 end fraction end cell row blank equals cell fraction numerator 8 square root of 2 minus 8 plus 2 times 2 minus 2 square root of 2 over denominator left parenthesis 2 square root of 2 right parenthesis squared minus 2 squared end fraction end cell row blank equals cell fraction numerator 8 square root of 2 minus 8 plus 4 minus 2 square root of 2 over denominator 8 minus 4 end fraction end cell row blank equals cell fraction numerator 6 square root of 2 minus 4 over denominator 4 end fraction end cell row blank equals cell fraction numerator 6 square root of 2 minus 4 over denominator 4 end fraction space space space space space cross times open parentheses fraction numerator begin display style 1 half end style over denominator begin display style 1 half end style end fraction close parentheses end cell row blank equals cell fraction numerator 3 square root of 2 minus 2 over denominator 2 end fraction end cell row blank equals cell 1 half left parenthesis 3 square root of 2 minus 2 right parenthesis end cell end table end style$

Jadi, jawaban yang tepat adalah D.