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Question

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.


Solution

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

1229686_1323608_ans_c5f5faf63b6a4d27a620321198f37082.PNG

Mathematics

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