Three cubes with sides in the ration 3 : 4 : 5 are melted

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Three cubes with sides in the ration 3 : 4 : 5 are melted to form a single cube whose diagonal is 12√3 cm. The sides of the cubes are ?

1. 6 cm, 8 cm , 10 cm
2. 3 cm, 4 cm , 5 cm
3. 9 cm, 12 cm , 15 cm
4. None of these

Correct Option: A

Let the side of the cube be 3k, 4k and 5k, respectively.
So, volumes of these cubes are 27 k³, 64k³, 125 k³ respectively.
⇒ Volume of the new bigger cube = 27 k³ + 64k³ + 125 k³
= 216k³
So, side of the new cube = 6k
Since, diagonal of the cube = √(6k)² + (6k)² + (6k)²
= 12√3
⇒ 108k² = 432
⇒k = 2
So, sides of the three cubes were 6 cm, 8 cm and 10 cm respectively.