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 :
Options:
A . 10 cm
B . 15 cm
C . 20 cm
D . 30 cm
Answer: Option B 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
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