3 cubes of metal whose sides are in ratio 3:4:5 are melted and converted into a single cube whose diagonal is 18√3 cm. The sides of cubes are ____, ____, ____.

# 3 cubes of metal whose sides are in ratio 3:4:5 are melted and converted into a single cube whose diagonal is 18√3 cm. The sides of cubes are ____, ____, ____.

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### Solution:

Let the sides of the cubes be 3x, 4x and 5x.
Let the sides of the single cube be a.
As,
Diagonal of the single cube = $18\sqrt{3}$ cm
a$\sqrt{3}$ = $18\sqrt{3}$ a = 18 cm
Now,
Volume of the single cube = Sum of the volumes of the metallic cubes
${a}^{3}$ = ${\left(3x\right)}^{3}$ +  ${\left(4x\right)}^{3}$+  ${\left(5x\right)}^{3}$
${18}^{3}$ = ${27x}^{3}$ +  ${64x}^{3}$+  ${125x}^{3}$
${18}^{3}$ = ${216x}^{3}$ 6x = 18
x = 3
So, the Sides of the cubes are 3 x 3= 9 cm, 4 x 3 = 12 cm and 5 x 3 = 15 cm.
Hence, the Sides of the given cubes are 9 cm, 12 cm and 15 cm.

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