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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 -

Let the edges of threecubes (in cm) be 3x, 4x and 5x respectively.

So, the volume of thecube after melting will be = (3x)3 + (4x)3 +(5x)3

= 9x3 +64x3 + 125x3 = 216x3

Now, let a be the edgeof the new cube so formed after melting

Then we have,

a3 =216x3

a = 6x

We know that,

Diagonal of the cube= √(a2 + a2 +a2) = a√3

So, 12√3 = a√3

a = 12 cm

x = 12/6 = 2

Thus, the edges of thethree cubes are 6 cm, 8 cm and 10 cm respectively.

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