Matematika

Pertanyaan

ABC.DEF merupakan prisma dengan alas segitiga ABC. perbandingan Ab:BC:BE=3:4:5hitunglah panjang rusuk prisma jika volume 240cm^3

1 Jawaban

  • V = 1/2 x a x b x tinggi
    240 = 1/2 x 3n x 4n x 5n
    240 = 30n^3
    n^3 = 240/30
    n^3 = 8
    n = 2

    AB = 3n = 3x2 = 6 cm
    BC = 4n = 4x2 = 8 cm
    BE = tinggi = 5n = 5x 2 = 10 cm

    BC^2 = 6^2 + 8^2
    BC^2= 36+64
    BC^2 = 100
    BC =√100
    BC = 10 cm

    panjang rusuk prisma =
    2x ( 6+8+10) + (3 x10)
    = 2 x 24 + 30
    = 48 + 30
    = 78 cm

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