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27 May, 23:21

Lateral area of a right rectangular prism is 144 cm². Its length is three times its width and its height is twice its width. Find surface area in centimeters squared

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  1. 27 May, 23:38
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    Step-by-step explanation:

    Given that, the lateral area is 144cm².

    Length is 3 * width

    Height is 2 * width

    Let width be x

    Then length is 3x

    Height = 2x

    Given that lateral area is 144cm²

    The formula for lateral area of a rectangular prism is

    A_L = Base perimeter. * height

    A_L = Ph = (2L + 2W) •h

    144 = (2 * 3x + 2 * x) * 2x

    144 = (6x + 2x) * 2x

    144 = 8x * 2x

    144 = 16x²

    x² = 144 / 16

    x = √ (144 / 16)

    x = √9

    x = 3

    So, the width is 3cm

    Height is 6cm

    Lenght is 9cm

    So the total surface area of a rectangular prism becomes

    A = 2 (LW + LH + WH)

    A = 2 (9*3 + 9 * 6 + 3 * 6)

    A = 2 (27 + 54 + 18)

    A = 2 * 99

    A = 198 cm²
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