Question

three cubes of edges 3:4:5 are melted down to form a single cube of diagnol 12√3. find the edges of the three cubes

Answer 1

let proportionality constant x
now
3x,4x and 5x are side length of cubes.
according to question
sum of all three cubes volume =vol of big cube.
(3x)^3+(4x)^3+(5)^3=(L)^3
(27+64+125)x^3=(L)^3
216x^3=(6x)^3=(L)^3
so,
L=6x
now diagonal of big cube=12root3
6x root3=12root3
x=2
hence side length of cubes are 6,8,10
respectively.