Three cubes with sides in the ratio 3:4:5 are | vedclass

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(B) Let the sides of the three cubes be $3x, 4x,$ and $5x$.The total volume of the three cubes is $V = (3x)^3 + (4x)^3 + (5x)^3$.$V = 27x^3 + 64x^3 +

Vedclass · Accepted Answer

$6 	ext{ cm}, 8 	ext{ cm}, 10 	ext{ cm}$

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(B) Let the sides of the three cubes be $3x, 4x,$ and $5x$.The total volume of the three cubes is $V = (3x)^3 + (4x)^3 + (5x)^3$.$V = 27x^3 + 64x^3 + 125x^3 = 216x^3$.Let the side of the new single cube be $S$. Then $S^3 = 216x^3$,which implies $S = \sqrt[3]{216x^3} = 6x$.The diagonal of a cube with side $S$ is given by $S\sqrt{3}$.Given that the diagonal is $12\sqrt{3} 	ext{ cm}$,we have $6x\sqrt{3} = 12\sqrt{3}$.Dividing both sides by $6\sqrt{3}$,we get $x = 2$.Therefore,the sides of the cubes are $3(2) = 6 	ext{ cm}$,$4(2) = 8 	ext{ cm}$,and $5(2) = 10 	ext{ cm}$.

Three cubes with sides in the ratio $3:4:5$ are melted to form a single cube whose diagonal is $12\sqrt{3} \text{ cm}$. The sides of the cubes are

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