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2014-11-26T07:28:41+05:30

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Let the edges (dimensions) of block be a, b, and c.
     a*b : b*c : c*a = 2 : 3 : 4
 
       a * b = 2 k        b * c = 3 k          c * a = 4 k    for some k > 0

multiply all these :
           a * b * b * c * c * a  = a² b² c² = 24 k³

             volume of block = a b c =  9, 000  cm³

            Hence a² b² c² = 9, 000 * 9, 000  = 24 k³
 
                         k³ = 27,000,000/8
                 k = 300 / 2  = 150
 
         Hence a * b = 300          b * c = 450        c * a = 600
 
                 a = abc / b c = 9000 / 450 = 20 cm
               b =  abc / ca  =  9000 / 600  =  15 cm
             c =  abc / ab =  30 cm

so 15 cm is answer

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