Geometry

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Find the missing numbers for the dimensions and measures of a rectangular prism...

Length 5 m
Width ?
Height ?
Surface Area 94 m to the second power
Volume 60 m to the third power

Please answer the one's with a ?. Thank you.

  • Geometry -

    we know that
    w*h*5 = 60
    2*5*w + 2*5*h + 2*w*h = 94
    since w = 12/h, that gives

    10(12/h) + 10h + 2(12/h)(h) = 94
    120 + 10h^2 + 24h = 94h
    10h^2 - 70h + 120 = 0
    h^2-7h+12=0
    (h-3)(h-4) = 0
    h is 3 or 4, so
    w is 4 or 3

    The prism is 3x4x5

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