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

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Solution

The edges of the three cubes are in the ratio 3 : 4 : 5.

So, let the edges be 3x cm, 4x cm, 5x cm.

The diagonal of new cube is

We need to find the edges of three cubes

Here, volume of the resulting cube,

Let,

Edge of the resulting cube

So, diagonal of the cube, so

Hence,

Now;

The edges of the three cubes are,

The edges of the three cubes are .

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