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3 February, 17:56

The volume of a box (V) varies directly with its length (l). If a box in the group has a length of 30 inches, and the girth of 20 inches (perimeter of the side formed by the width and height), what is its height? Use k = 24. (Hint: Volume = length width height. Solve for length, and substitute into the equation for constant of proportionality.) ___ inches or ___ inches

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  1. 3 February, 18:25
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    Given:

    length 30 inches

    k = 24

    v = l * w * h

    volume varies directly w / the length: v = kl

    v = 24 * 30 = 720

    k = wh

    24 = wh

    w = 24/h or h = 24/w

    P = 2w + 2h

    20 = 2w + 2h

    20 = 2 (24/h) + 2h

    20 = 48/h + 2h

    48/h + 2h - 20 = 0

    h (48/h + 2h - 20) = 0

    48 + 2h² - 20h = 0

    2h² - 20h + 48 = 0

    2 (h² - 10h + 24) = 0

    2 (h - 6) (h - 4) = 0

    h = 6 or h = 4

    Since the height serves as the length in the perimeter equation, then its measure is 6 and width is 4.

    length = 30; width = 4; height = 6.
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