Matematika

Pertanyaan

segitiga siku siku ABC dimana AB=BC dan siku-siku di B, jika AC= 6akar2 - 6 cm , maka panjang AB= .. cm ?

1 Jawaban

  • Misal AB = BC = x
    AB^2 + BC^2 = AC^2
    x^2 + x^2 = (6√2 - 6)^2
    2x^2 = 72 - 72√2 + 36
    2x^2 = 108 - 72√2
    x^2 = 54 - 36√2
    x^2 = 9(6 - 4√2)
    x = 3√(6 - 4√2) cm
    BC = 3√(6 - 4√2) cm

    BC = 3√(6 - 2 . 2√2)
    BC = 3√(6 - 2√8)
    BC = 3√((4 + 2) - 2√(4.2))
    BC = 3(√4 - √2)
    BC = 3(2 - √2)
    BC = 6 - 3√2

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