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Cuboid: (l + b + h)^2 = diagonal^2 + surface area

This type of question, asked 2 times: CDS 2 2019, CDS 1 2023. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    CDS 2 2019

    Consider the following for the next two (02) items : The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.
    99
    What is the surface area of the cuboid ?

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    100
    If S is the sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S−3V)(S - 3V) equal to ?

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  2. Question 2

    CDS 1 2023

    60
    The length of a diagonal of a cuboid is 11 cm. The surface area is 240 square cm. What is the sum of its length, breadth and height ?

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