The length breadth and height of a rectangle box are in the ratio of $4 : 3 : 2$ . the total surface area of the box is $2548 c m^{2}$ . Find its length, breadth and height.

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Solution

Let length $= l = 4 x$ , Breadth $= b = 3 x$ and height $= h = 2 x$
Total surface area of a cuboid $= 2 (l b + b h + l h)$
$\Rightarrow 2548 = 2 (4 x \times 3 x + 3 x \times 2 x + 4 x \times 2 x)$
$\Rightarrow 1274 = 12 x^{2} + 6 x^{2} + 8 x^{2}$
$\Rightarrow 26 x^{2} = 1274$
$\Rightarrow x^{2} = \frac{1274}{26} = 49$
$∴ x = 7$ cms
$∴ l = 4 x = 4 \times 7 = 28$ cm
$b = 3 x = 3 \times 7 = 21$ cm and $h = 2 x = 2 \times 7 = 14$ cm
$∴$ length $= 28$ cm, Breadth $= 21$ cm and height $= 14$ cm

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