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Math question?

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Calculate the length of the diagonal for the given rectangular prism. It says length hight width

but in the lesson it says length hight deph how to i find the diagonal example

  • Math question? -

    how to get diagonal saying lenght hight width

  • Math question? -

    another simple name for "rectangular prism" is a box
    let the
    length be x
    width be y
    height be z

    By the diagonal of the box they want the line from a bottom corner to the opposite corner at the top
    (think of placing a stick inside the box, where would the longest stick go ?? )

    let the diagonal of the base be d
    d^2 = x^2 + y^2

    now look at the right - angled triangle formed by that diagonal, the height and our stick
    let the length of the long diagonal (our stick) be k
    then k^2 = d^2 + z^2 , but d^2 = x^2 + y^2
    so k^2 = x^2 + y^2 + z^2

    e.g. suppose you have a box which is
    12 cm by 10 cm by 8 cm
    the diagonal = √(12^2+10^2+8^2) = √308 or appr 17.55 cm

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