the sum of the volume of three cubes is equal to three times the volume of a cuboid. The sides of the three cubes are equal to the length, bredth and height of the cuboid respectively. prove that the cuboid is a cube itself.

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Solution

$Let side of one cube = length of cuboid = L Side of second cube = breadth of cuboid = B Side of third cube = Height of cuboid = H According to question, L^{3} + B^{3} + H^{3} = 3 LBH This is possible only when, L = B = H, or L = - B = - H Since distance can' t be negative . Therefore, L = B = H Hence, Cuboid is cube .$

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the sum of the volume of three cubes is equal to three times the volume of a cuboid. The sides of the three cubes are equal to the length, bredth and height of the cuboid respectively. prove that the cuboid is a cube itself.

Let side of one cube=length of cuboid=LSide of second cube=breadth of cuboid=BSide of third cube=Height of cuboid=HAccording to question,L3+B3+H3=3LBHThis is possible only when, L=B=H, or L=-B=-HSince distance can't be negative. Therefore, L=B=HHence, Cuboid is cube.