The dimensions of a rectangular box are in the ratio 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rate of Rs. 8 and Rs. 9.50 per square metre is Rs. 1248. Find the dimensions of the box in metres.
Options:
A . 2 m, 12 m, 8 m
B . 4 m, 9 m, 16 m
C . 8 m, 12 m, 16 m
D . None of these
Answer: Option C Let the length, breadth and height of the box be 2x, 3x and 4x respectively Then, surface area of the box : = 2 [2x.3x + 3x.4x + 2x.4x] = [2(6x2 + 12x2 + 8x2)] = 52x2 $$\eqalign{ & \therefore 52{x^2} = \frac{{1248}}{{1.50}} \cr & \Rightarrow 52{x^2} = 832 \cr & \Rightarrow {x^2} = \frac{{832}}{{52}} \cr & \Rightarrow {x^2} = 16 \cr & \Rightarrow x = 4 \cr} $$ Hence, the diameter of the box are 8 m, 12 m and 16 m
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