List the measurements of three different rectangular prisms that each have a surface area of 20 square units?

Question

List the measurements of three different rectangular prisms that each have a surface area
of 20 square units?

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Mary 2 weeks 2021-09-11T02:33:36+00:00 1 Answer 0

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    2021-09-11T02:34:47+00:00

    Answer:

    3 measurements of different rectangular prisms that each have a surface area

    of 20 square units is given as

    (4.5 × 1 × 1)

    (2 × 1 × 2.67)

    (2 × 3 × 0.80)

    Step-by-step explanation:

    A rectangular prism is a cuboid and the surface area of a cuboid with length, x, width, y and height, z, is given as

    S = 2xy + 2yz + 2xz

    S = 2[xy + yz + xz]

    So, the question asks us to list 3 different measurements of a rectangular prism with surface area of 20 square units.

    S = 2[xy + yz + xz] = 20

    [xy + yz + xz] = 10

    So, with a little of trial and error, we can vary the values of x, y and z to obtain 3 separate measurements that give a surface area of 20 square units.

    [xy + yz + xz] = 10

    Let x = 4.5, y = 1, z = 1

    (4.5×1) + (1×1) + (4.5×1) = 10, works!!!

    (x, y, z) = (4.5, 1, 1)

    [xy + yz + xz] = 10

    Again, we can fix arbitrary values for two sides and calculate for the last side.

    If x = 2 units, y = 1 unit,

    (2×1) + (1×z) + (2×z) = 10

    2 + 3z = 10

    3z = 8

    z = (8/3) = 2.667 units

    (x, y, z) = (2, 1, 2.67)

    [xy + yz + xz] = 10

    And lastly, if x = 2, y = 3

    (2×3) + (3×z) + (2×z) = 10

    6 + 5z = 10

    5z = 4

    z = (4/5) = 0.80 unit

    (x, y, z) = (2, 3, 0.80)

    Hope this Helps!!!

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