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Tom
Lv 7
Tom asked in Science & MathematicsMathematics · 5 months ago

If the diagonal of a CUBE =C then what is the length of each side of the cube?

3 Answers

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  • Tom
    Lv 7
    5 months ago

    Actually C would be the hypotenuse of a right triangle 1 unit (edge length) on its shorter side and Sqrt of 2(Side diagonal) on the other side meaning, C^2=( 1)+(Sqrt2)^2   --------C^2=3 -------- C= Sqrt3 if the edge length is 1 ----But what if C=1?  what would the edge length be?

  • ?
    Lv 7
    5 months ago

    let the side length of the cube be 1. put one corner at (0,0,0) and extend a diagonal through to (1,1,1). Using the distance formula, the length of the diagonal is sqrt(3). 

    if the diagonal is given as C, then the side length = C/sqrt(3)

  • 5 months ago

    Assuming corner to corner not diagonal of one side

    c^2 = a^2 + b^2

    a = length of one side

    b is diagonal of one side

    b^2 = a^2 + a^2

    b = sqrt(2)a

    c^2 = a^2 + 2a^2

    c^2 = 3a^2

    c = sqrt(3)a

    a = c/sqrt(3) = csqrt(3)/3

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