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29 July, 14:22

A pyramid has a rectangular base of length (3x + 1) cm and width xcm.

It also has a perpendicular height of 12 cm.

The volume of the pyramid is 96 cmº.

Given that the volume of a pyramid is one third of the area of the base

multiplied by the perpendicular height, find the dimensions of the base

of the pyramid.

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Answers (1)
  1. 29 July, 16:37
    0
    The dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3

    Step-by-step explanation:

    Given

    Rectangle Pyramid

    Base Length = 3x + 1

    Base Width = x

    Height = 12

    Volume = 96

    Required

    Dimension of the base of the pyramid

    Given that the volume of the pyramid is ⅓ of the base area * the height.

    This is represented mathematical as

    Volume = ⅓ * base area * height.

    Where

    Base area = width * length

    Base area = (3x + 1) * x

    Base area = 3x² + x.

    So,

    Volume becomes

    Volume = ⅓ * (3x² + x) * 12.

    Volume = (3x² + x) * 4

    Substitute 96 for volume

    96 = (3x² + x) * 4

    Divide both sides by 4

    96/4 = (3x² + x) * 4/4

    24 = 3x² + x

    Subtract 24 fr both sides

    24 - 24 = 3x² + x - 24

    0 = 3x² + x - 24

    3x² + x - 24 = 0

    Expand

    3x² + 9x - 8x - 24 = 0

    Factorize

    3x (x + 3) - 8 (x + 3) = 0

    (3x - 8) (x + 3) = 0

    3x - 8 = 0 or x + 3 = 0

    3x = 8 or x = - 3

    x = 8/3 or x = - 3

    Recall that

    Length = 3x + 1

    Width = x

    For any of the above expression, x can't be less than 0; so, x = - 3 can't be considered.

    Substitute x = 8/3

    Length = 3x + 1

    Length = 3 (8/3) + 1

    Length = 8 + 1

    Length = 9

    Width = x

    Width = 8/3

    Hence, the dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
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