three cubes of metal whose edges are in the ratio 3:4:5 are melted and converted into a single cube of diagonal 24{root3}. find the edges of the three cubes.
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let side of cube formed be A
therefore A{root 3}=24{root 3}
A=24
lets sides of first three cubes be B, C, D
edge of B = 3x
edge of C = 4x
edge of D = 5x
According to the problem
(3x)^3+(4x)^3+(5x)^3= (24)^3
27x^3+64x^3+125x^3=13824
216x^3=13824
x^3=64
x = 4
Edge of B = 3x = 12
Edge of C = 4x = 16
Edge of D = 5x = 20
therefore A{root 3}=24{root 3}
A=24
lets sides of first three cubes be B, C, D
edge of B = 3x
edge of C = 4x
edge of D = 5x
According to the problem
(3x)^3+(4x)^3+(5x)^3= (24)^3
27x^3+64x^3+125x^3=13824
216x^3=13824
x^3=64
x = 4
Edge of B = 3x = 12
Edge of C = 4x = 16
Edge of D = 5x = 20
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