If the areas of adjacent faces of a cuboid is inthe ratio of 2:3:4 and it's volume is 9000cm^3, then the smallest side is how much?

• 15 cm
  
  Let length=l, breadth=b, height=h cm.
  So area of adjacent faces are lb, bh and lh
  Given the ratio of adjacent faces = 2x : 3x : 4x
  Let lb=2x, bh=3x and lh=4x
  As product of areas of adjacent faces=lb*bh*lh=(lbh)^2=Volume^2=(9000)^2
  So 2x*3x*4x =(9000)^2
  => 24x^3 = (9000)^2 , x^3=9000*9000/24 or x=150
  So the areas of adjacent faces are 2x=300, 3x=450 and 4x=600 cm^2
  => lb=300, bh=450 and lh=600 cm^2
  Identifying the values for l,b, & h we get l=20, b=15, h=30 cm.
  Hence the smallest side is 15 cm.
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