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30 May, 19:41

Jada is using 84 one-centimeter cubes to build a rectangular prism. She wants the height of the rectangular prism to be 4 centimeters. She also wants the width to be shorter than the length. How many rectangular prisms with different dimensions could Jada build

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  1. 30 May, 22:55
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    One rectangular prism is possible with 7cm * 3cm * 4cm.

    Step-by-step explanation:

    Jada used number of cubes = 84

    Side of one small cube = 1 cm

    Volume of one small cube = 1 cm³

    Volume of 84 small cubes = 84 cm³

    She wants to build a rectangular prism with height = 4 cm

    Let the length of the prism = x cm

    and the width of the prism = y cm

    and x > y

    Volume of the prism = length * width * height

    = (x) (y) (4)

    = 4xy cm³

    If the volume of prism = volume of 84 small cubes

    Then 4xy = 84

    xy = 21

    Possible values of x = 3, 7

    and y = 7, 3

    But x > y

    So x = 7 and y = 3 will be the answer.

    Therefore, only one rectangular prism is possible with dimensions

    length = 7 cm, width = 3 cm, height = 4 cm.
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