Pertanyaan

Sebuah persegi dengan panjang diagonal cm. Keliling persegi tersebut adalah ….

Sebuah persegi dengan panjang diagonal $open parentheses fraction numerator 1 over denominator square root of 3 plus 1 end fraction close parentheses$ cm. Keliling persegi tersebut adalah ….

$fraction numerator square root of 6 plus square root of 2 over denominator 4 end fraction$
$fraction numerator square root of 6 plus square root of 2 over denominator 2 end fraction$

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Klaim

N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

Jawaban terverifikasi

Jawaban

keliling persegi

keliling persegi $equals 4 cross times s i s i equals 4 cross times fraction numerator square root of 6 plus square root of 2 over denominator 4 end fraction equals square root of 6 plus square root of 2$

Pembahasan

Misalkan sisi persegi = a Panjang diagonal pesegi Maka, Jadi keliling persegi

Misalkan sisi persegi =a

Panjang diagonal pesegi

Maka,

$Sisi straight space persegi equals fraction numerator panjang straight space diagonal straight space pesegi over denominator square root of 2 end fraction S isi straight space persegi equals fraction numerator fraction numerator 1 over denominator square root of 3 plus 1 end fraction over denominator square root of 2 end fraction Sisi straight space persegi equals fraction numerator 1 over denominator square root of 3 plus 1 end fraction cross times fraction numerator 1 over denominator square root of 2 end fraction Sisi straight space persegi equals fraction numerator 1 over denominator square root of 2 open parentheses square root of 3 plus 1 close parentheses end fraction Sisi straight space persegi equals open parentheses fraction numerator 1 over denominator square root of 6 plus square root of 2 end fraction close parentheses cross times open parentheses fraction numerator square root of 6 minus square root of 2 over denominator square root of 6 minus square root of 2 end fraction close parentheses Sisi straight space persegi equals fraction numerator square root of 6 plus square root of 2 over denominator 6 minus 2 end fraction Sisi straight space persegi equals fraction numerator square root of 6 plus square root of 2 over denominator 4 end fraction$

Jadi keliling persegi $equals 4 cross times s i s i equals 4 cross times fraction numerator square root of 6 plus square root of 2 over denominator 4 end fraction equals square root of 6 plus square root of 2$