Question

Three cubes of metal whose edges are in the ratio $3:4:5$ are melted and formed into a single cube where diagonal is $12\sqrt{3}cm$ Find the edges of three cubes.

Answer 1

Let the sides of the metallic cube be $3x,4x,5x$.

Now according to the problem, these cubes are melt to form a new cube.

Then the volume of the new cube be $(3^3+4^3+5^3)x^3=216x^3=(6x{)}^3.$

Then the side of the new cube be $6x$.

And its diagonal be $6x\sqrt{3}$ cm.

Then according to the problem,

$6x\sqrt{3}=12\sqrt{3}$

or, $x=2$.

Then edge of the three cubes be $6,8,10$ respectively.