The dimensions of a rectangular box are in the ratio of $2 : 3 : 4$ and the difference between the cost of covering it with sheet of paper at the rates of $R s 8$ and $R s 9.50 p e r m^{2}$ is $R s 1248$ . Find the dimensions of the box.

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Solution

Que. rectangular box $2 : 3 : 4$
length $= 2 x$
breadth $= 3 x$
height $= 4 x$

surface Area $= 2 (2 x .3 x + 3 x .4 x + 4 x .2 x)$

$= 2 (6 x^{2} + 12 x^{2} + 8 x^{2})$

$= 52 x^{2}$

$\to 9.5 \times 52 x^{2} - 8 \times 52 x^{2} = 1248$

$∴ 1.5 \times 52 x^{2} = 1248$

$∴ x^{2} = \frac{1248}{1.5 \times 52}$ $∴ x^{2} = 16 x = 4$

$\to l = 2 x = 8 c m, b = 3 x = 12 c m, h = 4 x = 16 c m .$

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