If the areas of three adjacent faces of a rectangular block are in the ratio of 2 : 3 : 4 and its volume is 9000 cu.cm; then the length of the shortest side is :

Solution (By Examveda Team)

Let lb = 2x, bh = 3x and lh = 4x
Then,
$$\eqalign{ & 24{x^3} = {\left( {lbh} \right)^2} = 9000 \times 9000 \cr & \Rightarrow {x^3} = 375 \times 9000 \cr & \Rightarrow x = 150 \cr} $$
So, lb = 300, bh = 450, lh = 600 and lbh = 9000
$$\eqalign{ & \therefore h = \frac{{9000}}{{300}} = 30 \cr & l = \frac{{9000}}{{450}} = 20\& \cr & b = \frac{{9000}}{{600}} = 15 \cr} $$
Hence, shortest side = 15 cm