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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 SQRT3 cm. Find the edges of the

three cubes


Let edges of 3 cubes be 3x xm, 4x cm and 5x cm

So, voulme of single big cube = [(3x)3 + (4x)3 + (5x)3 ]cm3
Again,  \sqrt{ 27x3 + 64x3 + 125x3}  = 12 \sqrt{3}
or, 216x3 = 432
or, x =  \frac{x}{  \sqrt[3]{2} }

So, edges of 3 cubes are 3 \frac{x}{ \sqrt[3]{2} } cm, 4  \frac{x}{ \sqrt[3]{2} } cm and 5 \frac{x}{ \sqrt[3]{2} } cm.
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