The dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its total surface area is 88 $m^{2}$ . Find the dimensions of the cuboid.

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Solution

Let length : breadth : height = 1 : 2 : 3
$\Rightarrow$ l =x , b = 2x , h = 3x
TSA of a cuboid = 2(lb+bh+lh)
$= 2 (x \times 2 x + 2 x \times 3 x + x \times 3 x)$
$= 2 (2 x^{2} + 6 x^{2} + 3 x^{2})$
$88 m^{2} = 22 x^{2} m^{2}$
$\Rightarrow x^{2} = \frac{88}{22} \frac{m^{2}}{m^{2}}$
$∴ x = \pm 2$
So the dimensions are $2 \times 4 \times 6$

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