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

Question: Three cubes with sides in the ratio 3 : 4 : 5 are melted fo form a single cube whose diagonal is 12√3 cm. The sides of the cubes are-

Solution:
Let, the sides of the three cubes be 3x, 4x and 5x.
Then, Volume of the new cube = (3x)³ + (4x)³ + (5x)³
= 216x³

Edge of the new cube, ‍a³ = 216x³
⇒ a = (216x³)^1/3
∴ a = 6x

The diagonal of the new cube = 6√3x

ATQ,
6√3x = 12√3
∴ x = 2

So, the side of cubes are (3 × 2) cm, (4 × 2) cm, (5 × 2) cm Or, 6 cm, 8 cm and 10 cm