Question

three cubes of a metal whose edges are in the ratio 3:4:5 are melted and converted into a single cube whose diagonal is 12✓3 cm. Find the edges of the three cubes​

Answer 1

Answer:

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 (33+43+53)x3=216x3=(6x)3.

Then the side of the new cube be 6x.

And its diagonal be 6x3 cm.

Then according to the problem,

6x3=123

or, x=2.

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